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<h2>HL Paper 2</h2><div class="specification">
<p>A non-uniform electric field, with field lines as shown, exists in a region where there is no gravitational field. X is a point in the electric field. The field lines and X lie in the plane of the paper.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by electric field strength.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is placed at X and released from rest. Draw, on the diagram, the direction of the force acting on the electron due to the field.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force per unit charge</p>
<p>acting on a small/test positive charge</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontally to the left</p>
<p><em>Arrow does not need to touch X</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>proton moves to the right/they move in opposite directions</p>
<p>force on each is initially the same</p>
<p>proton accelerates less than electron initially «because mass is greater»</p>
<p>field is stronger on right than left «as lines closer»</p>
<p>proton acceleration increases «as it is moving into stronger field»</p>
<p><em><strong>OR</strong></em></p>
<p>electron acceleration decreases «as it is moving into weaker field»</p>
<p><em>Allow ECF from (b)</em></p>
<p><em>Accept converse argument for electron</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the ground state. Photons are emitted and are incident on a photoelectric surface as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.49.40.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p>The photons cause the emission of electrons from the photoelectric surface. The work function of the photoelectric surface is 5.1 eV.</p>
</div>
<div class="specification">
<p>The electric potential of the photoelectric surface is 0 V. The variable voltage is adjusted so that the collecting plate is at –1.2 V.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy of photons from the UV lamp is about 10 eV.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the maximum kinetic energy of the emitted electrons.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>1</sub> = –13.6 <strong>«</strong>eV<strong>»</strong> E<sub>2</sub> = – <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13.6}}{4}">
<mfrac>
<mrow>
<mn>13.6</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> = –3.4 <strong>«</strong>eV<strong>»</strong></p>
<p>energy of photon is difference <em>E</em><sub>2</sub> – <em>E</em><sub>1</sub> = 10.2 <strong>«</strong>≈ 10 eV<strong>»</strong></p>
<p> </p>
<p><em>Must see at least 10.2 eV.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10 – 5.1 = 4.9 <strong>«</strong>eV<strong>»</strong></p>
<p>4.9 × 1.6 × 10<sup>–19</sup> = 7.8 × 10<sup>–19</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Allow </em>5.1 <em>if </em>10.2 <em>is used to give</em> 8.2×10<sup>−19</sup> <strong>«</strong>J<strong>»</strong>.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>EPE produced by battery</p>
<p>exceeds maximum KE of electrons / electrons don’t have enough KE</p>
<p> </p>
<p><em>For first mark, accept explanation in terms of electric potential energy difference of electrons between surface and plate.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4.9 <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Allow 5.1 if 10.2 is used in (b)(i).</em></p>
<p><em>Ignore sign on answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two equally spaced vertical lines (judge by eye) at approximately 1/3 and 2/3</p>
<p>labelled correctly</p>
<p><img src="images/Schermafbeelding_2018-08-13_om_14.47.13.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08.c.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>kinetic energy at collecting plate = 0.9 <strong>«</strong>eV<strong>»</strong></p>
<p>speed = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2 \times 0.9 \times 1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>0.9</mn>
<mo>×</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>9.11</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span><strong>»</strong> = 5.6 × 10<sup>5</sup> <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.</p>
<p style="text-align: center;"><img 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"></p>
<p>The following data are available for the lamps when at their working temperature.</p>
<p> </p>
<p style="padding-left: 90px;">Lamp specifications 24 V, 5.0 W</p>
<p style="padding-left: 90px;">Power supply emf 24 V</p>
<p style="padding-left: 90px;">Power supply maximum current 8.0 A</p>
<p style="padding-left: 90px;">Length of each rod 12.5 m</p>
<p style="padding-left: 90px;">Resistivity of rod metal 7.2 × 10<sup>–7</sup> Ω m</p>
</div>
<div class="specification">
<p>A step-down transformer is used to transfer energy to the two rods. The primary coil of this transformer is connected to an alternating mains supply that has an emf of root mean square (rms) magnitude 240 V. The transformer is 95 % efficient.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline <strong>one</strong> other electrical advantage of this system compared to one in which the lamps are connected in series.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how eddy currents reduce transformer efficiency.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the peak current in the primary coil when operating with the maximum number of lamps.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt {\frac{{\rho l}}{{\pi {\text{R}}}}} ">
<mi>r</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>l</mi>
</mrow>
<mrow>
<mi>π</mi>
<mrow>
<mtext>R</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{\pi \times 0.1}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mi>π</mi>
<mo>×</mo>
<mn>0.1</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em>For MP2 accept any SF </em></p>
<p><em>For MP3 accept only 2 SF </em></p>
<p><em>For MP3 accept <strong>ANY</strong> answer given to 2 SF</em></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{0.1}}">
<mi>A</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mn>0.1</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em>For MP2 accept any SF </em></p>
<p><em>For MP3 accept only 2 SF </em></p>
<p><em>For MP3 accept <strong>ANY</strong> answer given to 2 SF</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current in lamp = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{{24}}">
<mfrac>
<mn>5</mn>
<mrow>
<mn>24</mn>
</mrow>
</mfrac>
</math></span> «= 0.21» «A»</p>
<p><em><strong>OR</strong></em></p>
<p><em>n</em> = 24 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{5}}">
<mfrac>
<mn>8</mn>
<mrow>
<mn>5</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>so «38.4 and therefore» 38 lamps ✔</p>
<p> </p>
<p><em>Do not award ECF from MP1</em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>when adding more lamps in parallel the brightness stays the same ✔</p>
<p>when adding more lamps in parallel the pd across each remains the same/at the operating value/24 V ✔</p>
<p>when adding more lamps in parallel the current through each remains the same ✔</p>
<p>lamps can be controlled independently ✔</p>
<p>the pd across each bulb is larger in parallel ✔</p>
<p>the current in each bulb is greater in parallel ✔</p>
<p>lamps will be brighter in parallel than in series ✔</p>
<p>In parallel the pd across the lamps will be the operating value/24 V ✔</p>
<p> </p>
<p><em>Accept converse arguments for adding lamps in series:</em></p>
<p><em>when adding more lamps in series the brightness decreases</em></p>
<p><em>when adding more lamps in series the pd decreases</em></p>
<p><em>when adding more lamps in series the current decreases</em></p>
<p><em>lamps can’t be controlled independently</em></p>
<p><em>the pd across each bulb is smaller in series</em></p>
<p><em>the current in each bulb is smaller in series</em></p>
<p> </p>
<p><em>in series the pd across the lamps will less than the operating value/24 V</em></p>
<p><em>Do not accept statements that only compare the overall resistance of the combination of bulbs.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«as flux linkage change occurs in core, induced emfs appear so» <span style="text-decoration: underline;">current</span> is <span style="text-decoration: underline;">induced</span> ✔</p>
<p>induced currents give rise to resistive forces ✔</p>
<p>eddy currents cause thermal energy losses «in conducting core» ✔</p>
<p>power dissipated by eddy currents is drawn from the primary coil/reduces power delivered to the secondary ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power = 190 <em><strong>OR</strong> </em>192 «W» ✔</p>
<p>required power <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 190 \times \frac{{100}}{{95}}">
<mo>=</mo>
<mn>190</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>95</mn>
</mrow>
</mfrac>
</math></span> «200 <em><strong>or</strong> </em>202 W» ✔</p>
<p>so <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{200}}{{240}} = 0.83">
<mfrac>
<mrow>
<mn>200</mn>
</mrow>
<mrow>
<mn>240</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.83</mn>
</math></span> <em><strong>OR</strong> </em>0.84 «A rms» ✔</p>
<p>peak current = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.83 \times \sqrt 2 ">
<mn>0.83</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
</msqrt>
</math></span> <em><strong>OR</strong> </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.84 \times \sqrt 2 ">
<mn>0.84</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
</msqrt>
</math></span>» = 1.2/1.3 «A» ✔</p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A beam of electrons e<sup>–</sup> enters a uniform electric field between parallel conducting plates RS. RS are connected to a direct current (dc) power supply. A uniform magnetic field B is directed into the plane of the page and is perpendicular to the direction of motion of the electrons.</p>
<p style="text-align: center;"><img 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68PCZ93F+ri3Nsmr1y5MtT1zHbl6LPZbgH2H3UBr2OQYVFR7yHUHwEDBPQb3z/+8Y8ydepUA6IhBARSE3D7ryYZLAgggEBUBbhyEdWWp94IGCLg3hlqw4YN0r17d0Oiik4YXt9ARUfCn5qeOHFCxo8fL2VlZZKfn+9PoZTSTIA+24yDFwhkXMDrGCS5yHiTsEMEEHAFdAKszq94+eWXudOOi5Lhn14fEhkOJxS70zue6QRvnYehE75Z/BWgz/rrSWkIJCvgdQySXCQryvoIIOCLgE7gnjlzpkyYMIEJ3L6IplaI14dEaqWylSYW69evlyVLljDB2+fuQJ/1GZTiEEhSwOsYZM5FkqCsjgAC/ghUVFTIhRdeSGLhDyelGCagV+S0f2s/Z0EAAQSiJMCViyi1NnVFwBCB2tpamTFjhtTU1PCtbpbbxOsbqCyHZ/Xu9erc6NGj5fnnn5fBgwdbXReTgqfPmtQaxBJFAa9jkCsXUewV1BmBLArohFdNLPSEq2vXrlmMhF0jEKyA9m/t59rftd+zIIAAAlEQ4MpFFFqZOiJgkIA+z2LAgAGiD8tjyb6A1zdQ2Y/Q/gj0Vst79+6VxYsX218ZA2pAnzWgEQgh0gJexyBXLiLdPag8ApkVqK6uFr2Tzu23357ZHbM3fwS+2CxzcjuJfrC09V/uvWXyH/Vf+LOvEJWi/V37vfZ/FgQQQCDsAiQXYW9h6oeAIQI6LGT+/PnOt7cMhzKkUVIMI6dkk3wei0ks/r8v90t5rw1SMGaeVB35OsWSw7mZ9ne9aqH9n+FR4WxjaoUAAucESC7OWfAbAggEKLBo0SIpLi7meRYBGme16G79pPCxOVIiVbJi40FpzGow5u08Ly/P6f96HLAggAACYRYguQhz61I3BAwR0LtDbdmyheFQhrRHsGE0yAd1R+VksDuxsnR3eJQeDywIIIBAWAVILsLastQLAUME9Hacv/zlL7k7lCHtEWQYjZ8ektqGHLm6b650C3JHlpatw6P0WNC7R+lxwYIAAgiEUYDkIoytSp0QMEhAn1KsQ0K4z79BjRJAKI0N2+TZhWVSnVMo9998hfDh0jayHgdjxoyRV199te0VeBcBBBCwXIBb0VregISPgMkCOnn1oosukuPHj0v37t1NDjWysXndUrAZjN4tqt9Nsrih2btnXwyQotLHZebdt8iwnG+3tQLvnRXguEivKyTVZ9PbFVsjgEAbAl7HIF8utYHGWwgg4I+ATl597bXXSCz84TSmlGZ3i/pyv7xWUiAy5ocy9sZrZQiJhWc7aaKtxwWTuz2pWAEBBCwUILmwsNEIGQEbBPS+/jqJe8KECTaES4ypCuhdop56Xl674k2579b58uIBnnORCKUeF3p86HHCggACCIRJgOQiTK1JXRAwSKC0tFQWLFggPNPCoEYJKpTOl8qkBb+SR/uul6n/WCE7T3IjWi9qPS7KyspEjxMWBBBAIEwCJBdhak3qgoAhAtu2bZPPPvtMCgoKDImIMIIW6Jxzk8x7ZraM2VIqjyzfwa1oEwDPz893jhM9XlgQQACBsAiQXISlJakHAgYJ6Lexs2fPNigiQgleoLN0G/YP8kzpUNky+5/lyc1HeJBeAuh6nHD1IgEoVkEAAWsEuFuUNU1FoAjYIaDfwurJ0rp16+wIOOJRet31I+I8Gan+pEmTnGRcr2SweAvQZ72NWAOBIAW8jkGuXASpT9kIRFCAqxYRbHSqnJYAVy/S4mNjBBAwTIDkwrAGIRwEbBZwx47zDazNrUjsmRZwjxf3+Mn0/tkfAggg4KcAyYWfmpSFQMQFuGoR8Q5A9VMW4OpFynRsiAAChgmQXBjWIISDgK0CtbW1Tujut7Am1UPHh/Jf2wbaTlG3MaGvuseNexyZEBMxIIAAAqkIkFykosY2CCDQSuCVV16RBx98sNX7vIEAAokJ6NULPY5YEEAAAZsFSC5sbj1iR8AQgcOHDztPG77++usNiYgwELBPYOjQoc5xpMcTCwIIIGCrAMmFrS1H3AgYJKC3nS0uLuZp3Aa1CaHYJ6BP7dbjiNs429d2RIwAAucEeM7FOQt+QwCBFAS++uorOe+88+T48ePSvXv3FEpgEwQyI3DDDTfI22+/LZs2bZKxY8dmZqdJ7uXEiRNy0UUXyalTp0jW27Hzusd+O5vxNgII+CTgdQxy5cInaIpBIKoCerKmY8VJLKLaA+yot97m9cMPP3SCffTRR40NWo+jhQsXOkmQsUESGAIIINCBAMlFBzj8CQEEvAWWLVsmd911l/eKrIFAFgU0oWhoaHAiqK+vl82bN2cxmo53/cMf/lD0uGJBAAEEbBQgubCx1YgZAUMEdOLp0aNHZfDgwYZERBgItBaIv2qhf/3Tn/4kJl+90ONJjysmdrduS95BAAHzBUguzG8jIkTAWAF3IrexARIYAiJOIuFetXBBTL96wcRut6X4iQACtgkwodu2FiNe6wT020ednHno0CE5efKkdfF3FPCiRYukqqpKevfu3dFq/A2BrAnoVYvbb7+9aUhUfCAjRoyQd999N/4tY37XfzcKCwtl+/btxsRkSiBek0lNiZM4EAirgNcxyJWLsLY89cqagD5ht7KyUqZPn+48+VhPEF544QXZsWNH1mIKasdlZWUkFkHhUq4vAvFzLVoWaPLVC03YBw0aJDyxu2Wr8RoBBEwX4MqF6S1EfFYI6O0j9cm6mlToCcGECRNkwIAB0qdPH24naUULEmQYBfSqxS233OLMsWivfiZfvaiurhZNgHSIFMs5Aa9vTc+tyW8IIBCEgNcx2CWInVImAlER0Gc8VFRUOEmFngBs2LCBW7JGpfGpp/ECXbp0kZ/85CfN4tSriNOmTWt6z+RbKA8fPlzmz59PcnG2tfTfW731tSaEmnTl5eU1tSO/IICAOQJcuTCnLYjEMgH9cJs8ebIUFRXJ1KlTuUJhWfsRbjQFvL5xM01Fh1f+7Gc/i/wd2fTq8Pjx42XMmDEycuRI0fle+oWO/vvLggACmRXw+neUOReZbQ/2FhIBHW6hiYXOOdAPuK5du4akZlQjUQGdcKvfpMYv+jqd24fqCVQQZWq5LRdNjlNdtDy/y2zPLh3PVOtn0nY6xHLr1q0mhZSVWHTYqSYSixcvdia661Xi8vLyNvthVgJkpwgg0CRActFEwS8IJCagJzujRo1y7pKUn5+f2EasFToBfQjbzJkzm5IBPTnW1+k8nE0n/bdVps7lSXX5+OOPnW9840/S9aSstLQ01SKlvTI14U51OX78uDNHSRN3d9Hf9YYIfi6xWMzP4gIvS4cAvfXWW4Hvx/QdaJ8rKChoClOHs+lVjGPHjjW9xy8IIGCGAMmFGe1AFJYI6AmkXqnQbxK5/aoljRZQmPotqk7e12RAv8XXn/o6nWEaevLUskwNf9asWSnXQh/IplfY9CRdEwxNLPbs2SNLlizxtUxNgPS2xKkuejzpcaWJuyYV+p/WO50yU43FpO3cf2fik0OT4stULJdccons3bu3aXf6b/GWLVvkvPPOa3qPXxBAwAwB5lyY0Q5EYYmAnui88847zqV5S0ImzIAF9MR9xYoVcv/996eVBMSH6ZZ57bXXyrJly3wZdqcn63fffbdcd911zk0I/BjK55Z5wQUXyBtvvOFLwq1laoLRv39/0bsluSfX8T7p/O41VjidsoPaVhNCnbwc/819UPsytVxN4HXOhSbvubm5zk00xo0bx2R3UxuMuEIt4PXvKFcuQt38VM5PAf2mTCcRzp07189iKctiAe0T+/btk4EDBzo/9XW6i1um33cx2r17txOnzrXQIUh+LFpmEN8ca2Kxf/9++eijj/wI0/oyhgwZEvmhUXo86DwLTSx0mT17NomF9T2bCoRVgOQirC1LvXwX2LVrlzPG1++TPt8DpcCMCGgS4A6FWrt2bdNwpnQSDLdMrcCmTZtk2LBhzeZgpFoxdyjUmjVr5Nlnn20aIpVqebqdW6YOZXruued8KdMdCqVXLOKHSKUTZxi2HTp0aFpzZMJgoHXQf3t1eJ/+x3y3sLQq9QijAMlFGFuVOgUiUFNTIxMnTgykbAq1T0CHLun8CJ2Do4v+1Nf6fqrL+vXrnU11PoQOW/KjTD1Rd+dYaJl6UqYxpjNROr5MPeHzo0ydU+DOsdChUFqmm2Ck6hmW7bTd9Nkc6dzhKywW1AMBBMwXYM6F+W1EhIYI6BhDHU7ClQtDGoQwEIiQgE6Y79atW1pJYYS4qCoCCAQowJyLAHEpOjoC+q2qXrUgsYhOm1NTBEwS0Hk9ejMJFgQQQMB0AYZFmd5CxGeEgN5LXe/WwoIAAnYL6DduNi56K1a99SoLAgggYLoAyYXpLUR8RggcPHhQRo4caUQsBIEAAtET0KumeqekqD/vInotT40RsE+A5MK+NiNiBBBAAIEICujTurk9bwQbniojYJkAyYVlDUa42RHQsc7f//73s7Nz9ooAAgiISL9+/eT3v/89FggggIDRAiQXRjcPwZkk0LNnT5PCIRYEEEhBIBaLpbCVGZtcccUVsnfvXjOCIQoEEECgHQGSi3ZgeBsBBBBAAAGTBJjUbVJrEAsCCLQn0KW9P/A+AgikJ5Dtu9LY/A1tevJsjUD7Al73Z29/y+z/RSd1v/fee6JPctcH67EggAACJgqQXJjYKsQUGoF/+7d/y0pdfvzjH2dlv+wUAQSCFZg9e7Z88sknltwau1FO1m+RtRVPy9TF1Wdgcoqk9NePyQN/myfd2qVKbbvG+lUyoe8yGbxpgzw9tkeL0v8kO5+ZLLfunyLvrSyUi9sct/FnqV9VJH3XjJe69VMkr811WhTLSwQQaCXAodOKhDcQQAABbwG9Jah+gxy/6Ot0bhV64sSJQMrUclsu9fX1Ld9K+LWW53eZ7dml45lwhSxaUYdGHTp0yIqIG4+sk4fHPCw1vf5Fjp6OSSz2Fzm6boR8cO9t8nDVR9LYTi1S3a6d4s6+fYEM+VGhXL3qN7Lxwz+3vWrjIdm65qBMuf8muZKzo7aNeBeBBAQ4fBJAYhUEEECgpcDmzZtl5syZTcmAnhzra30/1WXHjh1tlllZWZlqkfLxxx/L+PHjmyU95eXlUlpaalSZx48flz59+si2bdua4tLfCwsLm17zizjPujh58qQFFH+WDzf+RlbJrXLv1Gslxznb+LbkjJgqjy3oL6uKV8iWL9pKL1Ldzpuk85U3yf1TDsqarYfaTGwaP/ydrPmgQO4e10c4OfL2ZA0E2hPg+GlPhvcRQACBDgSKiopk0KBBTjKg3+JrYqGv9f1Ul4KCglZlalmzZs1KtUgZPHiwlJWVOSfpehVAE4s9e/bIkiVLjCqzd+/esnXrVhk1apSTYGhiofWuqqpKOc62NrR9LpLeEltvjW3+8h3Jm7JWYkeflLHnt3Gq0fChHPr06zaqkep2bRQlX8iBVVMlN/deKdveII2d+8i4uwvkg5fWy+6TLRObY7KlokK+/vkkGdFWvG0Vz3sIINCmQBtHfJvr8SYCCCBgjYB+05/OsJ9EK1pcXCxXXXWVXHfddc5PfZ3uEl/mN9984yQB6U7ezc/PdxIMPXH/3e9+Z3SZboIxffp0J7HQpIPlnEBoboldMF5GXfmdcxVL9LeEt9PEYpaMnS+yYPNSmTUiRzpLZzl/xCT5ufxW1m5vMVTwi/dl40sXyz0/GtjBXJBEg2Q9BKItQHIR7fan9giEUqBbt24yefJkKSkpCTTJ0KFQ+/btk4EDBzo/9XW6i1um3hnIz2X37t1OnJp06RAkP5YgytS4+vfvL/v37w/kadTZvotbuu49evSQLVu2pFtM1rZvPPKmPD1/f9LzGpLb7vO4xKJMpvQ7/1x9uw2UH91zsby08X35oundr+XIW1Xy2oS/l5tTSXiayuEXBBBQAZIL+gECCIROQMfp19TUyMiRIwNLMtw5FjoUau3atU3DmdJJMNwytUE2bdokw4YNazYHI9WGcodCrVmzRp599tmmIVKplrfaDB4AACAASURBVKfbBVGmOxSqurq62RCpdOIM27bu7WitrNfJvfLivCfl4H2/kgWTLk38BCSp7f4in24sk3+cul6uXjBb7otPLBy078iVN/+9THitSt46cnZYVuNB2bhit9x29w3t3EXKSm2CRiBrAiQXWaNnxwggEKSADiUKMsnQeQyaWLhDofSnvtb3U13Wr1/vbKrzITR+P8rUE3V3joWW6Q6RSmeidBBl6nwQd46FDoXSON0hUql6hnm7dJLYrLic3CurfnanzJeH5H/Ou+nsBO8EIkl6u71Sufj/ydCSG+WD+eWyzk0g4nbV+eIb5O7bdsuKjQedid3ORO6vfyJ3jPD3amHcLvkVgUgJdIq1mN1m8wOGItVyVDajAjq8Ztq0aUndW16PpWw+56LFoZ1RLxN3pidjevK+aNEiGTNmjHNFgPH8JrZUsDGF4TMulX+PglXtuPTGhm3y7NwHpFQekc3P3SP9uiX2vWay2zV7zsWYY7JqwliZ37u8jedaNMrJnc/KrfO+KyvWF8qXv/oHmdf9KVk/pV/iV1M6rjJ/RSDUAl7/jvIQvVA3P5WLsoAe/CxtC+hTjtO5FWvbpfKuLQK2Hxv6ID07lq+lYfNTctdNK0RKymXLP0+SvIQSi1S3i1PpnCd3PDlbXhr+pCy5+4YWD9XrLN2GTJB75AnZuuN7Urf8Yrm/5goSizg+fkUgHYHEvj5IZw9siwACWRHQKxf8d8ZAJzAvXbrUaQf9qa+xoX/Y2gey8g9K0jvVqwPPyV03/VLqppTLy08VJphYpLpdywA7S7dh/yDPlPaSxU+8JDtb3nq28xVy8/095aU5T8lrtxXKuIu/3bIAXiOAQIoCJBcpwrEZAgiYL6DPn9CJxxdddJETrCYVOo/B7zsxmS9BhGESGDBggOzdu9fsKjXWy9p5paL3tWpYdZv0/lYn0StG5/4bLnM2HxORP0v9qjukU6ezrxPeLpHqXyBD7pwiU+pK5ZHlO6T5owe/LReP+5GMqLtQHrhjqMTdTyqRglkHAQQ6EGBYVAc4/AkBBOwU0KTilVdekYceesi5YqFJBQmFnW3pd9R6cqtXLGxe9FbLxi+d+8mUjUdlSgKBOg/ba1qxR8LbtSy6c94U2RhrKsj5c+eLC6XiaDtPeT9/rDx9dGzLYniNAAJpCpBcpAnI5gggYJ7AlClTZNy4cc7wJ5IK89qHiBBAAAEEwivAsKjwti01QyCyAuvWrWP4U2RbP52Kfy1HqoolN3eebP6isYOCvpaGnS/JnBtzzw7zyZUb56yU13c2OLc27WBD/oQAAgiEXoDkIvRNTAURQAABBBIRaDzyhvxL8XPS4LGyrjf/1pdF7lsnR0/HJHZ6pzzda6v8461LZUuHSYlHwfwZAQQQCIEAyUUIGpEqIIAAAggkJtDufAvnKdD/Qw72HeZR0J/lw42/kVVX/1Sm3jPizMPgOufIiIcflQVX18jGHSc8tufPCCCAQLgFSC7C3b7UDgE7BRqq5N5md5Y5c5eZK5/ZKd/YWSOiNlrgT7Jz+VyZ3+UBmXfXFR6RnpTDdQclZ/Bl0iv+E7RzD7ls8F/kpY3vyxctSmhs2C6/nnPz2SFUV8u9z2yUeufWqMdk85zh0unmRVK1sUzuzT17N6Ub58ivdx6RL+o3yjP3Xn1mu9x7pWw7w65a0PISAQQMFIj/p9HA8AgJAQRCK9DYIDt/PUdudJOIG+fIqs31Z24XmVMov27jOR0fPjJMTLkLxeHDh0Wf+h2/6Gt9P9VF73IVRJlabsulvr6+5VsJv9by/C6zPbt0PNuqUOsH6OlzFf5VHvnVZVL+3yfKpd9qa6u49xqPyaHao3FvNP+1ofaQfBo3XaPxSJVMHzZJXpT7pe7L0xL7crWM/uARGfPwOjnirle9RJZuvlQeqz8tsdOHZdO1tXLf8N7Sb+GHcsOinRKLfS77F3SR0kkLZd2Rr5vvkFcIIICAYQKmfE4bxkI4CPgj8OMf/9ifgsJWSuNHUjX9Fin+5gFZd/QvMiKni5w88JL8bOxtsq38DVlZeKnxT8vdvHmzvP3227JkyRLp2rWrkxTMnDlTrr/+eikqKkqpxXbs2CGvvvpqqzIvv/xymTdvXkplfvzxxzJjxgypqqqS3r17O2Xosz/27NkjK1euNKZMvV1wnz59ZOvWrZKfn+/EtW3bNpk1a5Zs3749pTgT2ujkDln+yP+Wv/v3f5XCi78tninXyaNS90GDyOBESj87hEruk02PuU+nvkp+cu+tMv+m38jGOdfIZVpMzn3yz01/z5Hh44ZJzlPflQWPTZUROfpwt29L3qh8ubphmbxb94X8TSK7Zh0EEEAgSwJcucgSPLsNv0C2n/5rrnCjfLFlhRSv6h938tRZuvW7R5a+fKusL15hxaRYTSAGDRokmlDot/j6U1+nmlhoexUUFLQqU9/XE+xUl8GDB0tZWZkUFhY6V1XcxEKTolSXIMrUxEcTi1GjRokmFW5ioUlRYIsmuQ8/KP/r7x6VB4Zd4P9uGg/J1jVbRa6+Unp3cz9uO8v5Y5+Uo7G1MiWvq//7pEQEEEAgywLuv3ZZDoPdI4BAdAROyI6N1dKQc6Vc1ku/lXWXztKt95VydUO1NZNi9WnfV111lVx33XXOT32d7hJf5jfffNN0FSOdcvVKgCYYeuL+u9/9zugy3QRj+vTpza62pFP/trf9Wo6sK5Xig3fLMw8Ml4QfS9ctV/pendN2kam+2yz5SLUQtkMAAQTMECC5MKMdiMICgc8++8yCKC0KseEpuem73zo7yfXMRNZv9Z0q1RZVQecJ7Nu3TwYOHOj8bDlfIpWquGX6/fC/3bt3O3HqXAsdguTHEkSZGlf//v1l//798tFHH/kRZrMymu4W1XhQNq6okoYtP5fh/83th12l79RXRZy+2VtuXnWg9XMrnInbuc3KjH/RaqJ3/B/5PW0BnYOjfdiPYy3tYCgAAQTaFCC5aJOFNxFoLjBy5Ej5wx/+0PxNXqUnUFAhdfqMgFYTt3fI02N7pFd2BrbWkxt3KNTatWubhjOlc9Ljlqnhb9q0SYYNG+bsI50ytSx3KNSaNWvk2WefbRoilQ5TEGW6Q6Gqq6ubDZFKJ852t+3cT6ZsPNqi/30ldRW3i+Q8Kps+Pywbp/RrY+5PN+nd9wppOXFbnInef5Kr++aeuwrS+TIZ9dNRIh98KIedu0OdiaaxfpXc3ClXbl71f+V0uwHyh3gBPQb0apZe2XvhhRdk9OjRztC5+HX4HQEEzBAguTCjHYgCgQgJdJfhNxdIzge7ZG9D/J1v9K49ZXJjpztkVf2fjffQYUY6x8IdCqU/9bW+n+qyfv16Z1N3krgfZeqJuk7edst0h0jpHIxUlyDK1G+kdW6JO/Fc43SHSKUaZ1vbtb5bVFtrdfTed+TKm/9epnxQJgtf3Hvm7maNDbL92adk/gd3yJyf5MUlJN+RKydMl0f7rpUnFm2SBr07VOMR2fLiGqkeM1uevKO/eN2cqqNIovS3iooK0RsbrFu3ThYvXizPP/+801/STbyjZEhdEciYQKzFIqJf5LAggEC8wNatW2OzZ8+Of4vf0xE4fSj22pQBsZyi8ti7R/8Si8VOx76sey1WMuYHsTGl78a+TKdstkWgA4GOP+O+itVV3B6TnEdjmz4/fbaUs+/JsFjJps/Ovvd5rG5TRaxkTE5My9P/copKY6/tOBpzt4oP4fTRd2MvlhScXTcnNqakMrbD6fefxTaVDItJQUWsrmnD07HPNz0ay5HbYxV1XzUVc7quIlZwNoaFCxfG9N+kKC36729dXV2zKk+bNq3Ve81W4AUCCAQi0PG/o7FYJ91rfCaj3+q0eCv+z/yOQCQFdIxvSUmJ861ZJAGCqPTJetm8tkKemLpYtmj5OUVSWj5T7p407MxTj4PYJ2VGXiAMn3H6b9G0adMkLy8vMu2pdZ44cWLTbYr1ioUOjXKvdEUGgooiYICA17+jJBcGNBIh2CGgB9OpU6ecZxrYETFRIoBASwGvD8WW65v4OorJRW1trfO8Fh122LNnT2fehbaNDpFiQQCBzAp4/TvKnIvMtgd7s1hg4cKFsmvXLotrQOgIIBCGK/N6JfW8886LVGPqs1V0nkVNTY0z10JvsvH4449HyoDKImCLAFcubGkp4sy6gN7JRj/YUn1SctYrQAAIIBAKAa9vDUNRyQ4qEfX6d0DDnxDIiIDXMciVi4w0AzsJg8DQoUOdORf6NGYWBBCwU0A/FFkQQAABBIITILkIzpaSQybQtWtXmTt3rixfvjxkNaM6YRQ48yyFMw8n1BPqc//lyo1zVsnm+i/CWO3Q10mHROlkbhYEEEDAVAGSC1NbhriMFJgwYYJz9UKHSLEgYL5AjhRU7JfT8Q8qPL1Tnu5VI5PHzJOqI/HPGTG/NkR4RuDCCy+EAgEEEDBWgOTC2KYhMBMF9OrFyy+/7Ewo1Id+sSBgnUDnHBkx9V65R6pkxcaDos91Y7FHYO/evTJgwAB7AiZSBBCInADJReSanAqnK6D3ltfbIeoTjvX2iCwI2CmQK4Mv6xH3NGk7a5Fs1LbfLerkyZPSrVu3ZKvN+ggggEDGBEguMkbNjsIkkJ+f79wWccaMGVJZWSn6QCeWaAnolauW7a6v07mipTcL8LvMVq3S2CDbK6rk2Oxn5Z/G9Gj150Te0DjburGBzgdIdWnPLh3PVGMxeTu9cnHFFVeYHCKxIYBAxAVILiLeAah+6gJ63/UNGzY4J5Puk2LbOuFKfQ9sabLA5s2bZebMmU3JgJ4c62t9P9Vlx44dbZapCWxqS4NUT+0v34qf0P2tXPmbn1fJwU//IF+eSm1Q1Mcffyzjx49vlkiVl5dLaWlpamGKyPHjx6VPnz4SP59Jf9crhH4utt8tShO4Hj1SSwr9dKQsBBBAoD0Bkov2ZHgfgQQEunfv7jz3oqqqSo4ePSoXXXSRTJ8+XfS1ngS0/BY6gSJZxRKBoqIiGTRokJMMaFKpiYW+1vdTXQoKClqVqWXNmjUrxSLbmNAd+1zqXrtPZHGx3L98h5xMoWRNrN2hgXplQROLPXv2yJIlS1Io7cwmvXv3lq1bt8qoUaOcBEMTC623Hkss5wRef/11USsWBBBAwFQBHqJnassQl5UCmkzU1dU5J0l6svXCCy/IxIkTRedpXHDBBdKvXz8r6+UGrXfL0kntLOcE9CR7xYoVcv/996eRBJwrT39zy7z22mtl2bJlKZnrrWgn9J0vUrFZ1k/p13xuReMBWTVhrEz94D7ZdGCBjD0/te+ZNAG4++675brrrpOKioqU4mxec3ESC00w+vfvL9XV1b6fSOuVC1vnXegXFnp1aOXKlS3ZIvXa5jaMVENR2dAKeB2DXUJbcyqGQBYE9MRbv9XV/3TRkwD9ZvfUqVNy6NAh0cmYti7vvPOOM5FUv11nOSOgyeS+fftk4MCBzk99nW7y5ZapV8UCWzr3kMsG54p8kN4edu/e7dRdT3p1WJNf36hrYrF//3756KOPfCszvZqasbX+G3L55ZebEQxRIIAAAu0IkFy0A8PbCPgl4J5w6dUL2xc9iSS5ONOKmgS4Q6GKi4udoUH6WocGpZpguGXqHjZt2uRcDUi3zDb7XOMxOVR7VHLuGSfDU7xq4Q6FWrNmjezatcuZG6FDmNz+3uZ+Pd50h0LpFQtNLPQKhg6V0hso+LXYetVC66/Hn+1XP/1qR8pBAAFzBVK7Fm5ufYgMAQQCEtB76+tQL5YzAjp0SedYaGKhi/7U1/p+qsv69eudTd0ExY8yW8fyhdSvq5SXqofKz+8YKue3XsHzHT35d+dYaCKlJ/9a73QmX+sVPneOhSYoWqY7B8MzoIisoOY84yIijU01EbBYgDkXFjceoSOQaQGvcZaZjof9tS9wZs7FVKlutUqOjCl5XP7pjlvk1mE5zeditFo3fG/Y3Ic1dh1imeqVsbC0ps1tGJY2oB7RFvA6BhkWFe3+Qe0RSEpg2rRpztCMMAzxSqriFq7cOW+KbIxNsTBy/0LWYUT6XIiWS8s7UKVzxaVl2UG91rro8Rf1xCIoX8pFAAH/BEgu/LOkJARCL6DDfvRkjeQi9E0digrqUCu9NfB//dd/NavPbbfd1vT6yiuvTGs4V1NBAf+ix50efywIIICA6QLMuTC9hYgPAYMEhgwZInrXKBYEbBAYO3as/PVf/3W7ofbq1UueeOKJdv9u0h8OHDggevyxIIAAAqYLMOfC9BYiPgQMEtCHxemDAm2+445BnISSAQF9Yro+i+PTTz9ttTe9avH+++9bMdRoxIgRsmHDBgn0FsWthMx8w2u8t5lRExUC4RHwOga5chGetqYmCAQuoCc2+lBAHf/NgoANAnr14pJLLmkVqnvVwoY5DHq85ebmkli0akXeQAABEwVILkxsFWJCwGABnfza1iRZg0MmtIgLPPXUU6LJRPzSrVs3J1GOf8/U3/V4GzdunKnhERcCCCDQTIDkohkHLxBAwEtAn0btPo/Ba13+joAJAi2vXth01UL99HjTBwqyIIAAAjYIMOfChlYiRgQMEtCnSJ933nncb9+gNiEUb4H4uRc2zbXgeGvdtl7jvVtvwTsIIOCngNcxyJULP7UpC4EICOgY9YULF8quXbsiUFuqGBYB9+rFBRdc4Nwhyoa5Fmqvx9ns2bOtmHQelr5CPRBAID0Bkov0/NgagUgKDB8+XGpqaiJZdyptr4DOvfje975nzVwLldbjjPkW9vY5IkcgigIMi4piq1NnBNIUcG9Je+rUKSu+UdVLuCwItCdg8q2Vte8eP36cO0XFNZ7XkIy4VfkVAQQCEPA6BrlyEQA6RSIQdgG9Je20adMYGhX2hqZ+WRWora11jjOebZHVZmDnCCCQpADJRZJgrI4AAmcEbr/9doZG0RkQCFDgzTffFD3OWBBAAAGbBBgWZVNrESsCBgnYNDSKYVEGdRwDQzFxWJR7lyiGRLXuMF5DMlpvwTsIIOCngNcx2MXPnVEWAghER0CHauhdbPRuNvn5+UZX3MSTR1PAvD4kTIkzanG4d4liSFTUWp76ImC/AMOi7G9DaoBA1gQmTpwor7/+etb2z44RCKuAHld6fLEggAACtgmQXNjWYsSLgEECQ4cOlS1btogOkWJBAAF/BPR40uNKjy8WBBBAwDYBkgvbWox4ETBIQB9EVlRUJG+88YZBUREKAnYL6PGkx5UtD/qzW5voEUDAbwEmdPstSnkIREzg8OHDUlhYKNu3b49YzcNRXeZcmNeOI0aMkKqqKundu7d5wRkQEX3WgEYghEgLeB2DXLmIdPeg8gikL6AnQIMGDZJt27alXxglWCDQKCfrt8hvn7lXcjt1Ev2Q6dQpV26cs1KqNtfLSQtqYHKIehzp8URiYXIrERsCCHQkQHLRkQ5/QwCBhATuu+8+efHFFxNal5XsFmg8sk4eHvOQ/Pu3ZsjO0zHRO3HFYgdkxbiT8vrk2+Rnq/aSYKTRxHoc6fHEggACCNgqwLAoW1uOuBEwTECHcrz88suSl5dnWGSE05GA1+Xt5tsek81zxstNtQ9K3fopktfs66k/S/2qIuk7/0rZdGCBjD2/2R+bF8OrNgXq6+tl8uTJDDFsU+fcm8n12XPb8RsCCPgj4HUM8q+/P86UgkDkBebOnSu//e1vI+8QaoDGY3Ko9mg7VfyO5E1ZK7GjT5JYtCPk9XZ1dbXoccSCAAII2CzAlQubW4/YETBIQJ8oPHr0aNmwYYPw4C+DGsYjFK9voJpv/rUcqfq5XHPbcyJFpbJk4nAZWHCD5HXje6rmTsm/sumJ98nXzt8tkuuz/u6b0hBAQJy5dh09nJbkgl6CAAK+CZSXlztlFRcX+1YmBQUrkPyJ2hdS/x8VsvDen0tlgxtbgZRU3C83jxonY/POd9/kZxICHDuJYyXfZxMvmzURQMBbwOsYJLnwNmQNBBBIUMD99vX48eNcvUjQLNureX1ItB/f19Kw8y35Px/9SQ6+/pTMrtwrIgOkqGK1PDdlgHRrf0P+0kKA46YFiMfL1PusR8H8GQEEEhLwOgZJLhJiZCUEEEhUgG9gE5UyYz2vD4mEozx5QKqeeFhuW/xdqairlCl530l406ivyDGTXA/wrc8mt1vWRgCBswJexyDJBV0FAQR8FeBbWF85Ay/M60MiPoDG+lUyoe8yGbxpgzw9tkf8n5zfz/x9vkjFZlk/pZ8wE6MVUas3OF5akXi+kUyf9SyMFRBAIGkBr2OQf/uTJmUDBBDoSEAncy9dulReeeWVjlbjbxYKdL7yOvlpwVF5aeP78kW78Y+Sn466jMSiXZ/mf9DjRI8XboLQ3IVXCCBgrwDJhb1tR+QIGCtw1113SWVlpRw+fNjYGAksBYHOeXLHs0/J3770sDz0TJXsbPj6bCE6/+IlefT+J+Xr0kfkDoZEJYSrx4ceJ3q8sCCAAAJhESC5CEtLUg8EDBLQb2H1fv1LliwxKCpCSV+gs3Trd6/8684XpbD7u/JI7l85tyTs1OmvZNiSP8g1//ym/PsjI5jMnSC0Hh96nHDVIkEwVkMAASsEmHNhRTMRJAL2CbjPveCp3Wa3ndfYWbOjtzc692ncNTU10rVrV3srkoXI6bNZQGeXCMQJeB2DXLmIw+JXBBDwT0BPmMrKyqSkpMS/QikJgZAI6HGhxweJRUgalGoggECTAMlFEwW/IICA3wL5+fnSs2dPqaqq8rtoykPAWoHq6mrnuNDjgwUBBBAImwDDosLWotQHAcME3OEfGzZsYGy5YW2j4Xhd3jYwZKtD0lvPjh8/XhgumHoz0mdTt2NLBPwQ8DoGuXLhhzJlIIBAuwJ5eXlSVFQky5cvb3cd/oBAVAT0ONDjQY8LFgQQQCCMAly5CGOrUicEDBNwJ3c///zzMnjwYMOii3Y4Xt9ARVvH39rX1tbKjBkzhEnc6bnSZ9PzY2sE0hXwOga5cpGuMNsjgICngE5a1cTil7/8pWiiwYJA1AS032v/1+OASdxRa33qi0C0BEguotXe1BaBrAnoFYsRI0bIq6++mrUY2DEC2RLQfq/9nyt32WoB9osAApkSYFhUpqTZDwIIOFctRo8e7Xx7y0mWGR3C6/K2GVHaHYV7UwOGQ/nTjvRZfxwpBYFUBbyOQa5cpCrLdgggkLSAOzxKx50zPCppPjawUED7+eTJkxkOZWHbETICCKQmQHKRmhtbIYBAigJ6xWLSpEnOA8RSLILNELBGQB+Up/2dK3XWNBmBIoBAmgIkF2kCsjkCCCQvMGvWLNm+fbvow8RYEAirgPZv7efa31kQQACBqAgw5yIqLU09ETBM4PDhw1JYWOg8vbt3796GRRedcLzGzkZHwt+auv2bh+X566ql0Wf9N6VEBJIR8DoGSS6S0WRdBBDwVaCqqkoqKytl9erV3J7TV9nEC/P6kEi8JNZ0BXSexcyZM2XChAlOAu2+z09/BOiz/jhSCgKpCngdgwyLSlWW7RBAIG0BvXKht+fUceksCIRFQPvz5ZdfTmIRlgalHgggkJQAyUVSXKyMAAJ+C7jzL/QqBgsCtgswz8L2FiR+BBBIV4BhUekKsj0CCKQt4I5P16cXc1edtDmTKsDr8nZShUV85draWtHbLGuizDyi4DoDfTY4W0pGIBEBr2OQKxeJKLIOAggEKqAnYppY6ImZJhosCNgmoP1W+68OiSKxsK31iBcBBPwU4MqFn5qUhQACaQnokJJly5YxwTstxeQ29voGKrnSorm2TuC+8847paioiHkWGegC9NkMILMLBDoQ8DoGuXLRAR5/QgCBzAoUFBTIuHHjnDvt8ATvzNqzt9QE3DtDab/VGxSwIIAAAlEXILmIeg+g/ggYJlBcXCwXXnghd5AyrF0Ip20BHQal/VX7LQsCCCCAgAjJBb0AAQSME3j88cflP//zP6W8vNy42AgIAVdA+6f2U+2vLAgggAACZwRILugJCCBgnEDXrl1lyZIlsmfPHhIM41qHgFRAEwvtn9pPtb+yIIAAAgicEWBCNz0BAQSMFdDx7KNHj3YmyjLsJJhm8pqYF8xe7S5VEwt9snxNTQ2JRRaakj6bBXR2iUCcgNcx2CVuXX5FAAEEjBLQb4T1mQHuRFkSDKOaJ5LBaFKh/2m/5IpFJLsAlUYAAQ8BkgsPIP6MAALZFdBnBpBgZLcN2PsZAfeKBQ/Jo0cggAAC7QuQXLRvw18QQMAQARIMQxoiwmGQWES48ak6AggkJcCE7qS4WBkBBLIl4CYYb731FpO8s9UIEd2vJhba77hiEdEOQLURQCApAZKLpLhYGQEEsimgCcbq1au5i1Q2GyFi+9bEQu8Kpf1O+x8LAggggEDHAtwtqmMf/ooAAgYKuE9F1oeX6TMGmFibeiN53fUj9ZLt3lL72C9+8Qv54x//yO1mDWtK+qxhDUI4kRPwOga5chG5LkGFEbBfQJMJfb7ABRdcIDNnzhQ9EWRBwC8BN3nV/sVzLPxSpRwEEIiKAMlFVFqaeiIQMgFNMObNmyeDBg1ynoVx+PDhkNWQ6mRDQPuRPltF+5X2L66KZaMV2CcCCNgswLAom1uP2BFAwBHYtm2bzJo1S8rKyiQ/Px+VJAS8Lm8nUZT1q9KP7GhC+qwd7USU4RXwOgZJLsLb9tQMgUgJ1NfXy+TJk0UftFdUVBSpuqdTWa8PiXTKtmlbfTCeTt5++eWXJS8vz6bQIxcrfTZyTU6FDRPwOgYZFmVYgxEOAgikJqAnhHqr0LfffltKSkqYh5EaY+S20vkV2l+032j/IbGIXBegwggg4LMAyYXPoBSHAALZE9BbheoE3EsuucQZN69XM1gQaE9A+8edd97p9BftN9xqtj0p3kcAAQQSF2BYVOJWrIkAAhYJuOPn586dK4WFhRZFntlQvS5vZzaazO1Nr1IsWrSIeTqZI/dtT1Hts74BUhACGUupmgAACkxJREFUaQp4HYMkF2kCszkCCJgroHf+0edg6PMwNMno3r27ucFmKTKvD4kshRXYbk+cOOEkFfr8Cn2OBVcrAqMOrOCo9dnAICkYgRQFvI5BhkWlCMtmCCBgvoA7TGrAgAEyfvx40asZLNEV0PbXfqD9gWFQ0e0H1BwBBIIV4MpFsL6UjgAChgjo+HqduDtixAh54IEHuIpxtl28voEypPnSCkOvVixfvly2b98uixcvZtJ2WprZ3zgKfTb7ykSAQPsCXscgVy7at+MvCCAQIgG9C9Dq1audYTD67XV1dXWIakdV2hPQdtb21qtY2v7cDao9Kd5HAAEE/BHgyoU/jpSCAAIWCbhXMfREc+bMmZEed+/1DZRFzdosVJ1vo0OftK25WtGMxvoXYe2z1jcMFYiMgNcxyJWLyHQFKooAAq6AJhXr1q2TkSNHSp8+fUQfoKbPO2CxX0DbUdtT21XbV9uZqxX2tys1QAABewRILuxpKyJFAAGfBfQWtcePH5e9e/c6z8VgwrfPwBkuTttv9OjRTntqu3IL4gw3ALtDAAEERIRhUXQDBBBAQMQZPqMTvnWJ0jAar8vbNnQOd5hb1NrOhrYJIsYw9NkgXCgTgUwJeB2DJBeZagn2gwACVgjot9+lpaXOUJpp06aFfkiN14eEyY2mScULL7zgJIazZ8+W/Px8k8MlNp8EbO6zPhFQDAJZFfA6Bkkusto87BwBBEwU0HH769evdx62NmbMGAlzkuH1IWFi+7hJxZYtW5yHI06YMEG6du1qYqjEFICAjX02AAaKRCBrAl7HIMlF1pqGHSOAgOkCUUgyvD4kTGojkgqTWiN7sdjUZ7OnxJ4RCE7A6xgkuQjOnpIRQCAkAppkvP3227Js2TKnRmEaguP1IWFCE7pD1TSWBx98UK6//nquVJjQMFmKwYY+myUadotARgS8jkGSi4w0AztBAIGwCOiJ7osvvih79uxxhuTosKnu3btbWz2vD4lsVUyfqq3DnhYtWiSDBg2S++67jzkV2WoMw/Zrap81jIlwEAhMwOsYJLkIjJ6CEUAgzAI6REef/vzQQw/JwoUL5Yc//KEMHjzYuip7fUhkukK1tbXy5ptvymOPPSZLly6VgoKC0E+qz7Sx7fszrc/a7kn8CCQr4HUMklwkK8r6CCCAQJxA/JCpo0ePSnFxsYwdO9aap357fUjEVTWwX/Vp2ps3b5by8nLJzc1l6FNg0uEo2IQ+Gw5JaoFAagJexyDJRWqubIUAAgi0Emh5kqwPcTM90fD6kGhVSZ/ecK2qqqrExqTMJwaKSUEgW302hVDZBIFQCngdgyQXoWx2KoUAAtkW0OE9W7dulcrKSufbeE00Bg4caNzQKa8PCT8d1eT9998XN6EoKiqSUaNGGWfiZ50py3+BTPZZ/6OnRATsF/A6Bkku7G9jaoAAAoYLuN/S6x2n9KFvOkdj+PDhctVVV2V9+JTXh0Q6tFrvffv2yY4dO2TdunXOxGy905PpV3PSqTPbBi8QZJ8NPnr2gID9Al7HIMmF/W1MDRBAwCIBvQvS/v37Zffu3c5VDQ190qRJ0q9fPxkwYEDGJy97fUgkQ6uT3Pfu3SsHDhxwkgndVq9ODBkyRPr372/1XbWScWDdYAX87LPBRkrpCIRTwOsYJLkIZ7tTKwQQsEQgPtnQ29vqlQ19IrjeflUnN2vC0aNHj8BOzL0+JNpi1JiPHTvmJBI6X6Jl3JpMXHrppVm/KtNW7Lxnv0Aqfdb+WlMDBMwR8DoGSS7MaSsiQQABBBwBvQJw6NAh+fTTT50TeH3ew3vvvSf68D5dRo4c6fzUxEOXdJKPtj4k3ORBy9YrEbq88847zs/S0lK55pprRJ/vofvv1auXXHbZZRm/4uIEw/8iKdBWn40kBJVGIEsCXscgyUWWGobdIoAAAskI6C1vP/nkEzl16pQcPHhQTp482XTi7yYfbnluEuK+7uinJgu6vv50Fzd50NeaQHTr1k2+//3vS8+ePaVPnz48HduF4mdWBLxObLISFDtFIEICXscgyUWEOgNVRQCB8Au4SUiiNe3bt6/U1dWRNCQKxnpZF/A6scl6gASAQMgFvI5BkouQdwCqhwACCHQk4PUh0dG2/A2BbAjQZ7Ohzj4ROCfgdQx2PrcqvyGAAAIIIIAAAggggAACqQuQXKRux5YIIIAAAggggAACCCAQJ0ByEYfBrwgggAACCCCAAAIIIJC6AMlF6nZsiQACCCCAAAIIIIAAAnECJBdxGPyKAAIIIIAAAggggAACqQuQXKRux5YIIIAAAggggAACCCAQJ9Al7nd+RQABBBCIoIDeVpAFAQQQQAABPwRILvxQpAwEEEDAUoFYLGZp5ISNAAIIIGCiAMOiTGwVYkIAAQQQQAABBBBAwEIBkgsLG42QEUAAAQQQQAABBBAwUYDkwsRWISYEEEAAAQQQQAABBCwUILmwsNEIGQEEEEAAAQQQQAABEwVILkxsFWJCAAEEEEAAAQQQQMBCAZILCxuNkBFAAAEEEEAAAQQQMFGA5MLEViEmBBBAAAEEEEAAAQQsFCC5sLDRCBkBBBBAAAEEEEAAARMFSC5MbBViQgABBBBAAAEEEEDAQgGSCwsbjZARQAABBBBAAAEEEDBRgOTCxFYhJgQQQAABBBBAAAEELBQgubCw0QgZAQQQQAABBBBAAAETBUguTGwVYkIAAQQQQAABBBBAwEIBkgsLG42QEUAAAQQQQAABBBAwUYDkwsRWISYEEEAAAQQQQAABBCwUILmwsNEIGQEEEEAAAQQQQAABEwVILkxsFWJCAAEEEEAAAQQQQMBCAZILCxuNkBFAAAEEEEAAAQQQMFGA5MLEViEmBBBAAAEEEEAAAQQsFCC5sLDRCBkBBBBAAAEEEEAAARMFSC5MbBViQgABBBBAAAEEEEDAQgGSCwsbjZARQAABBBBAAAEEEDBRgOTCxFYhJgQQQAABBBBAAAEELBQgubCw0QgZAQQQQAABBBBAAAETBUguTGwVYkIAAQQQQAABBBBAwEIBkgsLG42QEUAAAQQQQAABBBAwUYDkwsRWISYEEEAAAQQQQAABBCwUILmwsNEIGQEEEEAAAQQQQAABEwVILkxsFWJCAAEEEEAAAQQQQMBCAZILCxuNkBFAAAEEEEAAAQQQMFGA5MLEViEmBBBAAAEEEEAAAQQsFCC5sLDRCBkBBBBAAAEEEEAAARMFSC5MbBViQgABBBBAAAEEEEDAQgGSCwsbjZARQAABBBBAAAEEEDBRgOTCxFYhJgQQQAABBBBAAAEELBQgubCw0QgZAQQQQAABBBBAAAETBUguTGwVYkIAAQQQQAABBBBAwEKBTrFYLObG3alTJ/dXfiKAAAIIIIAAAggggAACbQrEpRDN/t4l/lV7K8Wvw+8IIIAAAggggAACCCCAQFsCDItqS4X3EEAAAQQQQAABBBBAIGkBkoukydgAAQQQQAABBBBAAAEE2hIguWhLhfcQQAABBBBAAAEEEEAgaYH/D4DvEJ0VLyAgAAAAAElFTkSuQmCC"></p>
<p>The magnetic field is adjusted until the electron beam is <strong>undeflected</strong> as shown.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, on the diagram, the direction of the electric field between the plates.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following data are available.</p>
Separation of the plates RS
= 4.0 cm
Potential difference between the plates
= 2.2 kV
Velocity of the electrons
= 5.0×10<sup>5</sup> m s<sup>–1</sup>
<p> </p>
<p>Determine the strength of the magnetic field B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The velocity of the electrons is now increased. Explain the effect that this will have on the path of the electron beam.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>direction indicated downwards, perpendicular to plates</p>
<p><em>Arrows must be between plates but allow edge effects if shown. Only one arrow is required.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{V}{d} = 55\,000">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mi>V</mi>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mn>55</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
</math></span> «Vm<sup>–1</sup>»</p>
<p>B = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{55\,000}}{{5 \times {{10}^5}}} = ">
<mfrac>
<mrow>
<mn>55</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
</mrow>
<mrow>
<mn>5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 0.11 «T»</p>
<p><em>ECF applies from MP1 to MP2 due to math error.</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong> </em></p>
<p>magnetic force increases<br><em><strong>OR<br></strong></em>magnetic force becomes greater than electric force</p>
<p> </p>
<p>electron beam deflects “downwards” / towards S<br><em><strong>OR <br></strong></em>path of beam is downwards</p>
<p><em><strong>ALTERNATIVE 2</strong> </em></p>
<p>when <em>v</em> increases, the <em>B</em> required to maintain horizontal path decreases<br>«but B is constant» so path of beam is downwards</p>
<p><em>Do <strong>not</strong> apply an ecf from (a). </em></p>
<p><em>Award <strong>[1 max]</strong> if answer states that magnetic force decreases and therefore path is upwards. </em></p>
<p><em>Ignore any statement about shape of path<br></em></p>
<p><em>Do not allow “path deviates in direction of magnetic force” without qualification.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A cable consisting of many copper wires is used to transfer electrical energy from an alternating current (ac) generator to an electrical load. The copper wires are protected by an insulator.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: center;"><img src="blob:https://questionbank.ibo.org/bd73db7f-3f45-4a7f-b356-67d8fed5fa2a"></p>
</div>
<div class="specification">
<p>The cable consists of 32 copper wires each of length 35 km. Each wire has a resistance of 64 Ω. The cable is connected to the ac generator which has an output power of 110 MW when the peak potential difference is 150 kV. The resistivity of copper is 1.7 x 10<sup>–8</sup> Ω m.</p>
<p>output power = 110 MW </p>
<p style="text-align: center;"><img 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YhFktXxjX+/23mRLJDPYpUcIpv3c8lqMUrG4gPSRaUYkayjUSoz5kpljVfksr0Oq2SRy70lSdIVqbEsV4JSRsC6ctxY1ih1BI+l5k5qt63kiFkiGN+TvF9D9IwEAgR8F3Bi3wkgZx7GZygXo2nIzN8GlxRIk7UNLpcPHucHqD92TYzHcf3UbpRU2QHLPBXKYciZ+TCMSjHiTIYJ2TkuPH/kU2zKz0eGKjU6P8WRujYYl03EWHUeZGB89iS4nz+G1k1m5Gd2O6kugfskkBQE2EKTIgx0QjMBz1nYiv4Fw7OX4JVTXwNIw8iCKrRaFwFnzuFiL1M00dp1V83FiOC9AHE/4AFkl/wh2uxMRwKDToAj+0EPAR3QTuA2nPt/hZKjs3Hg4g4sHHdvoMiraCo/D2CyRhNGWKxNOFw8BRwdaUTJ7INGgG130NDTcNQE0iZi1tOzeozQ/Q8/mVBgO4UvHOeBnEcxzagIvZjJ+QbXr94JMXMTZxwu1Q1bcXPXBccZE5YVPILMkNTIfAQFy0w4c/IzuLsW/gC4jrbqH8JQYIOz2/HQAviZBJKDAMU+OeJAL/okcD8mF67Axuz92PybRr/o+i6huXYf7OYN2LZ4Jv61wAKjfR9qmy/5n471udFS8yJW2872KNldVYmt9e1+wRfTP2tKUVdYgbXm0T3SAqNhXluBwsO/QEXNyYDgd8JZX4X1G4Dt2xYii70oDDceSjYCbKbJFhH6E5ZAmvEH2LJ3L57xVsOUboAh/TFs9i5F695VyM24B5nmNThUOx0fzh2PdDG3Pv45fDChCAcPlMHYrcRhsGxfgfzzv0aWSDf8xzieU43mmgUY10tvSBu3ADXNNZh9+Vd+24YRMDeMwprW3ViXO7Jb6fxAAslKwCAWHsXTOfEATJxNxNN93ZRNzroJle4cZduKf8gSwbiXsUz8K0cLJEACJEACiSNAsU8ca1oiARIggUEjQLEfNPQ0TAIkQAKJI0CxTxxrWiIBEiCBQSNAsR809DRMAiRAAokjwCdoE8c67pbEHX1uJEACJBCOAEf24ajwGAmQAAmkGAGKfYoFlNUhARIggXAEKPbhqPAYCZAACaQYAc7Zp1BA+aRyCgUziarCe0FJFAwNrnBkrwEes5IACZCAXghQ7PUSKfpJAiRAAhoIUOw1wGNWEiABEtALAYq9XiJFP0mABEhAAwGKvQZ4zEoCJEACeiFAsddLpOgnCZAACWggQLHXAI9ZSYAESEAvBCj2eokU/SQBEiABDQQo9hrgMSsJkAAJ6IUAxV4vkaKfJEACJKCBAMVeAzxmJQESIAG9EKDY6yVS9JMESIAENBCg2GuAx6wkQAIkoBcCFHu9RIp+kgAJkIAGAhR7DfCYlQRIgAT0QoBir5dI0U8SIAES0ECAYq8BHrOSAAmQgF4IUOz1Ein6SQIkQAIaCFDsNcBjVhIgARLQCwGKvV4iRT9JgARIQAMBir0GeMxKAiRAAnohQLHXS6ToJwmQAAloIECx1wCPWUmABEhALwQo9nqJFP0kARIgAQ0EKPYa4DErCZAACeiFAMVeL5GinyRAAiSggQDFXgM8ZiUBEiABvRCg2OslUvSTBEiABDQQoNhrgMesJEACJKAXAhR7vUSKfpIACZCABgIUew3wmJUESIAE9EKAYq+XSNFPEiABEtBAgGKvAR6zkgAJkIBeCFDs9RIp+kkCJEACGghQ7DXAY1YSIAES0AsBir1eIkU/SYAESEADAYq9BnjMSgIkQAJ6IUCx10uk6CcJkAAJaCBAsdcAj1lJgARIQC8EKPZ6iRT9JAESIAENBCj2GuAxKwmQAAnohYBBkiQp1FmDwRB6iJ9JgARIgAR0QiCMrOOecL6HSxgu3VA4dvLkSTQ0NKCqqmooVJd1JAFdEhD9dMyYMcjKytKl/4lwOuzIPhGG9Wrj7bffxg9/+EOMGjVKr1Wg3ySgewJOpxNlZWX42c9+BovFovv6JKICYUf2iTCsVxsZGRmYN28eli9fjpKSEjzwwAN6rQr9JgFdEhAiL8R+w4YNmDlzpi7rMBhOc2QfA/Vbt27BarVi1qxZmD59egwlMAsJkEB/CIg+pwyshNBzuqY/9PxpKfb9Z9YjR319PTweDxYtWhRskD0S8QAJkEC/CVy7dg2vv/46Dh48iJaWln7nZ4YuAlx62cUi5j2z2YzOzk7Mnj0bdrs95nKYkQRIoIuAuOkqpkynTJmC48ePd53gXkwEOLKPCVv4TGIU0tzcjIULF4ZPwKMkQAJ9EhB96ObNmxg/fjzE1I3YlOmbPjPyZEQCHNlHRBR9ArFCRxH6ixcvYsaMGRBTPEqjjb4kpiSBoUVAiPzOnTvx0EMP4bPPPpMrL0SeQj9w7YBiP3Asu5UkRiZ79uzBRx99JE/viJtK3EiABMITKC4ulk98/fXXXEoZHpHmo5zG0YwwcgFilC9GLGKUot6PnJMpSCA1CShTnuJ+F59ZSUyMObJPAGcxylcuR8WqAnEjl9M7CQBPE0lHQExpKtM1LpeLQp/ACHFkn0DYiikxpfPuu+/i+vXrfA2DAoV/hwQB0fbFirUlS5ZQ6BMccYp9goGHM8dL2nBUeCwVCAhx/93vfodp06bJT52nQp30WgdO4yRB5MQUj7ikFfP64hKXq3eSICh0QTOBbdu2YenSpXj88cflBw41F8gCNBHgyF4TvoHNLEb4f/zjH5Gfny+vMx7Y0lkaCcSfgBjJT5gwQb5Hpd6Pv2VaiESAYh+J0CCeFyMjMa8v5jf5Dp5BDARN90lAXIl+/PHH2L59u5zunXfeCS5I6DMjTyaUAMU+obj7Z0zdicS7unfv3t2/ApiaBBJAQPnNBw5KEgBbgwmKvQZ4icwqpnjEemTxBfDnP/8ZeXl5XM2QyADQVpCAeFZELCEWb57ku+SDWJJ+hzdokz5EfgfVD56IuVDlZq7oeNxIIFEExLvkxStBMjMz5QFHouzSjnYCHNlrZzgoJSjLNcWSNr7be1BCMCSMiitJh8MRvGfEm676DTtH9jqNnfLSNUXoxYMq4sVr4mcTxRcBNxLQQkC0IbEMeNiwYXjvvfeCRYn2pjwNHjzIHV0Q4M8S6iJMkZ0Uc6cTJ06Un04UUzziNbHslJG5MUV4AuJV3WKqRryYTD2FGD41j+qBAKdx9BAlDT6K0ZnJZAJfOKUBYopnVW64iqvCN998Mzhlk+LVHnLV4zROiodcjPjVT+emeHVZvX4SOH36dPCG6/vvv0+h7yc/PSXnyF5P0dLgq7jRJi7JxRs4eXNXA0idZxVr4sVP/Imf+lN+aEfnVaL7URLgyD5KUHpPJubvhdCLTeyLH0gXy+gWLFgAMbrjltoExJe9uIFfW1srL5ksLCxM7Qqzdj0IcGTfA8nQOiCW0o0ePVq+CSf2L1y4wAe2UqAJiHn4pqYmdHZ2YvXq1XKNxBUdb7amQHBjrAJH9jGCS5VsYimdIgBimZ0Q/Hnz5mHFihVcwqnTIIvYKQIvrtyUTYmz8pl/hxYBjuyHVryjrq364Rmxhv/y5cvyq2qVdf1RF8SEcSUgpuBOnDiBY8eOwWazyV/cYsqGy27jil2XhVPsdRm2xDqtTAmIn1IUK3vEqg2OEhMbA8WaeipGLKv95JNPIObfxXy8ck9GScu/JKAmQLFX0+B+RAJqsRGvYP7rX/+K73//+3wHf0RysSdQ1sGL0bv4shVfuhT22HkO1ZwU+6Ea+QGqt5hG+PTTT3H27Nng7+mK5X3ilcyc8uk/ZOVdNOfPnw+O1gVj9ef+l8ocJADwBi1bgSYC4kdVli9fHhR6UdhXX30l/5CFwWCQl3dqMpDimcW9ESHwYhP3RsRN8r1798qfxWsvxCYYizXxHM3LOPhfjAQ4so8RHLNFJiBETHmQS6QWq0TEj09v2LBBvtk7VB/qESP1Xbt2ySyefPJJ/PKXv+STq5GbE1NoJECx1wiQ2ftHQMz5f/nll/j73/8e/OELsTxQTPt861vfwhNPPBE83r+SkyO1mF9XRuBC1MUoXYzeGxoa8Je//EUWdcHg6tWrwd9qTQ7P6UWqE6DYp3qEdVI/IYhXrlzBN998ExR75UrgJz/5Cb73ve+hoqJCro0QUTHdITbxVxHXeFdVEWnxRlExhy5WwYgljuKGqXiJmBD0xx57DHv27JHvVwjhF6IuHlpLlI/xZsDy9UuAYq/f2A0Zz8UXgVrUxdy2WJmibC+99JIsumIp4po1a+RpInHuueeek5eIKr+RqqRfu3atLL5CoMWNZbGNHDkSP/3pT+X0QrwPHz4sT7OIc2IqSiw1Fcc/+ugjOf3jjz8eFPvQ6So5Af8jgSQjQLFPsoDQHW0EhPD+7W9/kwtRVgMpI3Kl5AkTJshfDmLkLUbpyhaaXvmsnOdfEtAzAYq9nqNH30mABEggSgJcehklKCYjARIgAT0ToNjrOXr0nQRIgASiJECxjxIUk5EACZCAnglQ7PUcPfpOAiRAAlESoNhHCYrJSIAESEDPBCj2eo4efScBEiCBKAlQ7KMExWQkQAIkoGcCFHs9R0+L7x4njlZvxVvO21pKSaK8nXAefRkVb7XDJ3t1G07bYhhMFWjq9B+J3tlOOOsrMMdggMFgQoFNKTP6ElI6Zcq1nZSOVrByFPsgiqG040NnSy2KNnwCb6pUu7MV1qLfoG0AKuRzvos1Tx3CpAMX4JVcOFI8he8CD7aTFGw7wbql9g7FPrXjy9rFTOA+jB75IEU+Zn7MmHQEJG46JXBFaizLlWAuk97cvlwyAhKMG6XGDq8kSXckV+vbUpnZKEEch0UqszZKjhvinFfqaNzoTy+fg2Qsa5Q6OhqlMmNgP0hESZsrlTVekSSpF5tf2qUyo1GyvGmXTtWWSWal3OU7JLujI1hajx3Zpj/fhzsCdYBRMpe9LbW67qiSi/ockLYvnxaoD+R6Wxsd0g2RKuC7v64Kh28kh3WRBONyafv/bJeWGwUHcW65tN0eyKey4N+95c8T8N+fXmHaITkarb0wFbl7YSPHo4chSfK6pNbeWA1ALMxlNUFecnyFCyE2RdsJMhTnVfEIH0elPQRYIrS9hKknDyUNAY7sk+7rt58ONb+HE6M2wCndgat5JWZk/gOX6tchd/4xjK1sg1eSIN34b2QfL4W59CAu+dKQmb8F7Y0bYcQiWB234KrMR2Z/zIbaHJEOwA37s9U4MPzfcUjY9F7EnnHvw7LSijZPX3PmIt86vIZn0eYVvjZhDfYgb8muQD4fPG27sGR+A9JX2f31EXV9YRjq5q7D623Xgcx8VLY3osxohMX6ObyubcjPDDRt91H86eNJ2OT0QhL59kzCnyyBfD3qfD+yivfD67DCglyUNV6BJJflQbvtP2FeejzI1Ot6EWOPlyJ7fk33+oWyUfxQ2/J9gfoVFuTVpmONowOS1IGm2WdRZK5A/aW76pSR90PtBWLRXPcJRm08Ccn7FZqfzUNmwOb8pu+g0nUHkuTFjdcexvGlT6G0/ovAfQ5hrq84CtQa207kGjFFnAhQ7OMENmHFGuej6EcPIwP3wpj1XWR0nsDLq+uRs2UjSmcY/dMQGdNQ/EoNlh3ehpebr2p3LdRmoERjWTk2LZyCDPE5zYi8J3JhbP4Qn7j6FjBj8UvYVjoTRtEaM6Zg4aZylDl+j/0t1wBcQ8v+38OxrAglSn1EXc1PY5mlHUc/uawSqjBVMz6DFzYtQFaGKLwf+dRFdbbi/zzfgsKdvwoyTTPOxH++UoMyx3ZU7Hd2+dALG3VxvnONeMN2H8peWIeFWeJrNhNTfvRvWIZ6vHHkfFdZ6ky97fdiz7js3/CjKZlA2reR9c8Z6Gx+A6ttU7FlUwlmGO8VAULGlGV4Zc98HF79BppVN7FjjWNvLvJ4chCg2CdHHAbICx86W4+hzm3C9Imju883Z5iQneNC3ZFP0TlA1vouJg0Z4ycjB+fhuOjpI6kROTMf9gu9kqqbr6ORX9kKV2UeLjc1yO+Ur6/fjfK5+Sixd72eWMka3XWD5W4AAAQ5SURBVN+bOONwoS+vuspRmE7FzGn/FIYp+lGWKPU2zp14H3ZMQvZ4+WvRb0pcnbjidTP4GlqP2OE2TsbEsULolS0QI7cdR1rFF2u4Ldo4hsvLY8lEgGKfTNEYMF/aUDV3DMQPfgf/pU9Fid09YBYSUZD79AVc9vngaX8LRaYRyJ77Kk5dF1NC30bBa/WwWvortLF4fReXL5xDX+T8fsZSdoLzuH+NuSPSu9qEwYD07BLYE+wGzQ0OgXsGxyytxpeAmIt/G8VZ9/dixpeg0X0v5qM8bJw+EWPhxP7SjThaeAAXdy/EOGV40tmE8jNuYHqUhcWc7F6MnTgZRpzrtQTZzzTgYq8pkuSExQrH4WJkKQxD3UrMJV+oVX5OEIHewp4g8zQzsATSkJn3BJYZP8fJs191n/v1tKB6zuTeHxCSp06MA+tOVKW5e06DeFxwnDFhWcEjyJT30WOqx3fjOgbg7kMUHvbFVPgJ5GSb/PcpoigNuB+TZ82DJXR6y9cOW4EJhgIbnMPElNtAxmIU8gosMJ75GGfd6vsn4ub3bzHHsBi2lHm4LqogDMlEFPtUC3vmLKzdORuHV7+Imha3X/A97ajf/AI2YBW2Lc5Cmrg5J8+ni8r7cNNzE760iZj19Cy4636Pd9vFEM8Hj/Mgtm6u7XMKYyDwuasqsbW+3T+H7jkL25pS1BVWYK15NJD5CAqWmWCv24fmgFD53CdRU/EL2NRzK/KXlf9HyHHTgz4XAPXX6cw8/PuWGSFM/X5WZW8IMI2+0LTJBSjf+BCqNu9Ck1ynu3A370Od/VFs37YQWfcMdCzSkGleiZ2Fx7G6YjdaZJv++G5evwvYvh6Le70KDK1XmLYTmoSfk5IAxT4pw6LFqXsxbuE2NO+ZjcvluUgX8/bDF6FhzEq07l2FXHlVCuAXnA6UZD+IB5/6H5zz3Y+sxVtgX/cPPD91BAyG8Zhv/QZPvbAJFi3uRMxrhLnsR3js/K+RJfv6YxzPqUZzzYLAlM1omH/+Kmpn/C/mmu6T55vHP/chJhS9igNluV2lp01CYfky3C2ZivQHi7H/3EC+BiITU4p/G8L0v+CYXQPHodIg0y5nIuyljUP+llq0PnMTm+U63QfT5pt4pnU31uWOhBj9D3gs0r6LhTUHsGf2lyiXbaZjuLkBY9bsw951M/pxZRKu7USoL08nBQH+Bm1ShGGIOiHm3acsxektTTjMVxIM0UbAaieKAEf2iSJNOyRAAiQwiAQo9oMIn6ZJgARIIFEEOI2TKNK0QwIkQAKDSIAj+0GET9MkQAIkkCgCFPtEkaYdEiABEhhEAhT7QYRP0yRAAiSQKAIU+0SRph0SIAESGEQCFPtBhE/TJEACJJAoAhT7RJGmHRIgARIYRAIU+0GET9MkQAIkkCgCFPtEkaYdEiABEhhEAhT7QYRP0yRAAiSQKAL/H9W4Tb7LzM/sAAAAAElFTkSuQmCC"></p>
<p> </p>
</div>
<div class="specification">
<p>To ensure that the power supply cannot be interrupted, two identical cables are connected in parallel.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The energy output of the ac generator is at a much lower voltage than the 150 kV used for transmission. A step-up transformer is used between the generator and the cables.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of each <strong>wire</strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the peak current in the <strong>cable</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the power dissipated in the cable per unit length.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the root mean square (rms) current in each cable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The two cables in part (c) are suspended a constant distance apart. Explain how the magnetic forces acting between the cables vary during the course of one cycle of the alternating current (ac).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest the advantage of using a step-up transformer in this way.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The use of alternating current (ac) in a transformer gives rise to energy losses. State how eddy current loss is minimized in the transformer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>area = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.7 \times {{10}^{ - 3}} \times 35 \times {{10}^3}}}{{64}}">
<mfrac>
<mrow>
<mn>1.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>64</mn>
</mrow>
</mfrac>
</math></span> «= 9.3 x 10<sup>–6</sup> m<sup>2</sup>»</p>
<p>radius = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{9.3 \times {{10}^{ - 6}}}}{\pi }} = ">
<msqrt>
<mfrac>
<mrow>
<mn>9.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mi>π</mi>
</mfrac>
</msqrt>
<mo>=</mo>
</math></span>» 0.00172 m</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>I</em><sub>peak</sub> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{{P_{peak}}}}{{{V_{peak}}}}">
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>p</mi>
<mi>e</mi>
<mi>a</mi>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>p</mi>
<mi>e</mi>
<mi>a</mi>
<mi>k</mi>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span>» = 730 « A »</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>resistance of cable identified as «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{64}}{{32}} = ">
<mfrac>
<mrow>
<mn>64</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2 Ω</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{a power}}}}{{35000}}">
<mfrac>
<mrow>
<mrow>
<mtext>a power</mtext>
</mrow>
</mrow>
<mrow>
<mn>35000</mn>
</mrow>
</mfrac>
</math></span> seen in solution</p>
<p>plausible answer calculated using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{2}}{{\text{I}}^{\text{2}}}}}{{35000}}">
<mfrac>
<mrow>
<mrow>
<mtext>2</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>I</mtext>
</mrow>
<mrow>
<mtext>2</mtext>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>35000</mn>
</mrow>
</mfrac>
</math></span> «plausible if in range 10 W m<sup>–1</sup> to 150 W m<sup>–1</sup> when quoted answers in (b)(ii) used» 31 «W m<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow <strong>[3]</strong> for a solution where the resistance per unit metre is calculated using resistivity and answer to (a) (resistance per unit length of cable = 5.7 x 10<sup>–5</sup> m )</em></p>
<p><em>Award <strong>[2 max]</strong> if 64 Ω used for resistance (answer x32).</em></p>
<p><em>An approach from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{V^2}}}{R}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
</math></span> or VI using 150 kV is incorrect (award <strong>[0]</strong>), however allow this approach if the pd across the cable has been calculated (pd dropped across cable is 1.47 kV).</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{response to (b)(ii)}}}}{{2\sqrt 2 }}">
<mfrac>
<mrow>
<mrow>
<mtext>response to (b)(ii)</mtext>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<msqrt>
<mn>2</mn>
</msqrt>
</mrow>
</mfrac>
</math></span>» = 260 «A»</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wires/cable attract whenever current is in same direction</p>
<p>charge flow/current direction in both wires is always same «but reverses every half cycle»</p>
<p>force varies from 0 to maximum</p>
<p>force is a maximum twice in each cycle</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if response suggests that there is repulsion between cables at any stage in cycle.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>higher voltage gives lower current</p>
<p>«energy losses depend on current» hence thermal/heating/power losses reduced</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>laminated core</p>
<p> </p>
<p><em>Do not allow “wires are laminated”.</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows how current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> varies with potential difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> across a component X.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlcAAAGSCAYAAADO9uQeAAAgAElEQVR4Ae29z4scSZrnvf9JJOQpExIk1DR5UtF015KVh0SjgygQ777voEqQGgqKYWCXylzVRTRUTxHJiKEFszuTotS1sANL5MLCDCXVBnvRQUOADnVIAubQSCIOQmiThBYiCZ4XiwiLsPDwx93c/HnMLSK/AUl4PG72+GMf+xHfNLcw/3eEFwiAAAiAAAiAAAiAgBiBfyfmCY5AAARAAARAAARAAAQI4gqNAARAAARAAARAAAQECUBcCcKEKxAAARAAARAAARCAuEIbAAEQAAEQAAEQAAFBAhBXgjDrulpvrdG7d+/qukF+EAABEAABEACBBglAXDUI37308+fPyYirR3945JpxDAIgAAIgAAIgsGQEIK4SqbDPb90aiatfffIJZq8SqROEAQIgAAIgAAIhBCCuQqgJ5zGzVgdffz0SVyedDmavhPnCHQiAAAiAAAjEJABxFZM2cy0za9Xv90fi6s9//jNh9ooBBTMIgAAIgAAILAEBiKuGK8nOWpkwzJor88LsVcOVgsuDAAiAAAiAQA0CEFc14ElktbNWxpcVV5i9kiALHyAAAiAAAiDQDAGIq2a4j67qzloZgxVX5hizVw1WDC4NAiAAAiAAAjUIQFx5wRvSef9HOrqzPRJA661N2j34gXqDj7PcwwH1vj+g3dbaJM027bc782lmqUdHZhG7WWtlX664srNX5h0vEAABEAABEACB5SEAceVRV8M3Hbq3sUm795/RYGgynFG/c592dx5S79wYhnTWvU9brT067JzSubEMntE3O5u0vndM/VGexQtlNwx1xZVJnT2/6AEWEAABEAABEACB1AhAXJXWyAfqH9+m9dZtetz/MEs9PKXHe1fpxvEpDektdQ+uZ4SUzfclnQwuZvkKjrLiqiApToEACIAACIAACCRKAOKqtGJe0cmdq7R+pU29OY00sd/p0OCiR0dX1mjroEtnjr+LXpuuta7TYfetY+UPIa54NjgDAiAAAiAAAstCAOKqtKZKxJURXe+6dLixRtfaPXL117B/TDdaV2m/86r0KiYBxJUXJiQCARAAARAAgaQJQFyVVs/k9t7GfeqeOYunzsaCajSj9apD+61FcUUDY4e4KkWMBCAAAiAAAiCwQgQgrjwqc7ygfZv2//b5eEH78A117++NfxVoZq4qiCszO1X099P//j+EPzBAG0AbQBtAG0AbKG4DHl/fjSWBuPJCn9mKYeMLOnr2Iz02a7HMrwHfX+7bgmYAWMYX4o5ba+AN3j4E0E58KMmlAW85lq4niCuXRpVjdxG7e+z4uCwL2tE5nUqPcAjeESA7lwBvB0aEQ/COANm5BHg7MAQPIa5KYdotFTJbMYzWU9lfAhZtxZDJV3C9ZV3Qjs5ZUKkKp8BbAWqBS/AugKNwCrwVoBa4BO8CODVOQVx5wFvYRPS8Tz+1v6Brdzv0ZrTG3W4iuk37xz/TOZnbiB063NmkrWma8gtBXJUzkkyBQUWSZrkv8C5nJJkCvCVplvsC73JGkilS5w1x5VXbM7E0XoxuHm3zI/VHu7NPHCw8/ibnETkl14K4KgEkfDr1zskVF3FzZHTs4K3DlfMK3hwZHTt463CFuNLhGuQV4ioIW3AmDCrB6IIygncQtuBM4B2MLigjeAdhC86UOm+Iq+Cqlc8IcSXPtMhj6p2Tix1xc2R07OCtw5XzCt4cGR07eOtwhbjS4RrkFeIqCFtwJgwqweiCMoJ3ELbgTOAdjC4oI3gHYQvOlDpviKvgqpXPCHElz7TIY+qdk4sdcXNkdOzgrcOV8wreHBkdO3jrcIW40uEa5BXiKghbcCYMKsHogjKCdxC24EzgHYwuKCN4B2ELzpQ6b4ir4KqVzwhxJc+0yGPqnZOLHXFzZHTs4K3DlfMK3hwZHTt463CFuNLhGuQV4ioIW3AmDCrB6IIygncQtuBM4B2MLigjeAdhC86UOm+Iq+Cqlc8IcSXPtMhj6p2Tix1xc2R07OCtw5XzCt4cGR07eOtwhbjS4RrkFeIqCFtwJgwqweiCMoJ3ELbgTOAdjC4oI3gHYQvOlDpviKvgqpXPCHElz7TIY+qdk4sdcXNkdOzgrcOV8wreHBkdO3jrcIW40uEa5BXiKghbcCYMKsHogjKCdxC24EzgHYwuKCN4B2ELzpQ6b4ir4KqVzwhxJc+0yGPqnZOLHXFzZHTs4K3DlfMK3hwZHTt463CFuNLhGuQV4ioIW3AmDCrB6IIygncQtuBM4B2MLigjeAdhC86UOm+Iq+Cqlc8IcSXPtMhj6p2Tix1xc2R07OCtw5XzCt4cGR07eOtwhbjS4RrkFeIqCFtwJgwqweiCMoJ3ELbgTOAdjC4oI3gHYQvOlDpviKvgqpXPCHElz7TIY+qdk4sdcXNkdOzgrcOV8wreHBkdexnvd+/eUb/f17l4Da9lcddwLZIV4koEo4wTiCsZjr5eUu+cXDkQN0dGxw7eOlw5r+DNkdGxl/E++Pprevr0qc7Fa3gti7uGa5GsEFciGGWcQFzJcPT1knrn5MqBuDkyOnbw1uHKeQVvjoyOvYj38+fP6fNbt3QuXNNrUdw1XYtkh7gSwSjjBOJKhqOvl9Q7J1cOxM2R0bGDtw5Xzit4c2R07EW8jbAyAivFV1HcKcQLcZVCLUxigLiKWxmpd06OBuLmyOjYwVuHK+cVvDkyOnaOt7kV+Nt793QuKuCVi1vAtYgLiCsRjDJOIK5kOPp6Sb1zcuVA3BwZHTt463DlvII3R0bHnsf7z3/+M/3qk0+SXMhuKeTFbc+l8A5xlUItTGKAuIpbGal3To4G4ubI6NjBW4cr5xW8OTI69jzeJ50OmYXsKb/y4k4pXoirhGoD4ipuZaTeOTkaiJsjo2MHbx2unFfw5sjo2LO8zdYL5rvIvKf8ysadWqwQVwnVCMRV3MpIvXNyNBA3R0bHDt46XDmv4M2R0bFnef/+22/pj0+e6FxM0Gs2bkHXIq4grjwxDgcv6MnB3kjRGxG0dech/dQ/m+UeDqj3/QHtttYmabZpv92h3uDjLE3JEcRVCSDh06l3Tq64iJsjo2MHbx2unFfw5sjo2F3eZrNQs9bKrLlK/eXGnWKsEFc+tXL+go52NmnrbofeDE2G99Rr36T1jfvUPTOGIZ1179NWa48OO6d0biyDZ/TNziat7x1Tf5Sn/EIQV+WMJFOk3jm5siJujoyOHbx1uHJewZsjo2N3eZt1Vma91TK83LhTjBfiyqNWLnptuta6SvudV9PU87a31D24nhFSH6h/fJvWW1/SyeBimq/oAOKqiI78udQ7J1dixM2R0bGDtw5Xzit4c2R07JZ3yhuG5pXcxp13LgUbxJVHLcwLqXGGOdtFj46urNHWQZecG4U0TnOdDrtvPa5Co9uJXgkTS5R6I+dwIW6OjI4dvHW4cl7BmyOjY19m3uY2oNkw9OXLlzpwFLymzhviyqfS2duCX9HJm49EZ1063Fija+0euXNUw/4x3cjMeBVdDjNXRXTkz6XeObkSI26OjI4dvHW4cl7BmyOjYze8l2HrhWzpU28nEFfZGmM+j4WSXaxu3p0ZqUGH9luL4opG9vnbiYz7kRniqoiO/LnUOydXYsTNkdGxg7cOV84reHNkdOwn//N/jRaxv379WucCSl5TbycQVx4VP3zToXsb27R//PNosTrRRxp0H9Bu6yYd9d7TWET5iSsjoIr+TIPBHxigDaANoA2gDcRoA3/1V39N5i/GtaSv4fH13VgSiKtS9JPF6tNfBk4yDE/p8d4mrd/p0AC3BUspppjAdPRlfCHuuLUG3uDtQ2AZ24nZeuGX136xFFsvZOsgdd4QV9kaW/j8ik7uXKX1K23quQuqyLF/wIL2BWxLYEi9c3IIETdHRscO3jpcOa/gzZGRt5utFx48+J284wgeU28nEFeljeCceu3PFsWVO3NFRVsx3KbH/Q+lVzEJsObKC5NYotQ7J1dQxM2R0bGDtw5Xzit4c2Rk7XbrBfCW5Wq9QVxZEgXv4zVXe3T4/QsajDYEzay5mm4iatdlDem836HDuY1HCy4wOQVxVc5IMgUGFUma5b7Au5yRZArwlqRZ7muZeJutF8xO7GbrhWWK262F1OOGuHJriz02YulHOrqzPVuMvnNAT3oDmm6+vvD4m03aPfgBj79hmTZ/IvXOyRFC3BwZHTt463DlvII3R0bO7m69AN5yXF1PEFcujYaPMXMVtwIwqIC3DwG0Ex9KcmnAW45lnqd3796NJgns1gvgnUepvg3iqj5DMQ8QV2IovRxhUPHCJJYIvMVQejkCby9MYomWhffvv/2W/vjkybTcyxL3NODJQepxQ1xla6zBzxBXceGn3jk5GoibI6NjB28drpxX8ObI1LebrRfMWiuz5sq+wNuSkH2HuJLlWcsbxFUtfJUzY1CpjKxWBvCuha9yZvCujKxWhmXgbZ4f+PTp07lyLkPccwFPPqQeN8RVXq01ZIO4igs+9c7J0UDcHBkdO3jrcOW8gjdHpp7dLGL/7b17C07AewGJiAHiSgSjjBOIKxmOvl4wqPiSkkkH3jIcfb2Aty8pmXQp87ZbL5jbgtlXynFnY3U/px43xJVbWw0fQ1zFrYDUOydHA3FzZHTs4K3DlfMK3hyZcPujPzwi85f3Au88KvVtEFf1GYp5gLgSQ+nlCIOKFyaxROAthtLLEXh7YRJLlCrvvEXsbqFTjduNMe849bghrvJqrSEbxFVc8Kl3To4G4ubI6NjBW4cr5xW8OTJhdrPOKruI3fUE3i4NuWOIKzmWtT1BXNVGWMkBBpVKuGonBu/aCCs5AO9KuGonTpG3EVV5i9jdwqYYtxsfd5x63BBXXM01YIe4igs99c7J0UDcHBkdO3jrcOW8gjdHppq9aBG76wm8XRpyxxBXcixre4K4qo2wkgMMKpVw1U4M3rURVnIA3pVw1U6cGu+iRexuYVOL242t6Dj1uCGuimov8jmIq7jAU++cHA3EzZHRsYO3DlfOK3hzZPztZYvYXU/g7dKQO4a4kmNZ2xPEVW2ElRxgUKmEq3Zi8K6NsJID8K6Eq3bilHiXLWJ3C5tS3G5cZcepxw1xVVaDEc9DXEWETUSpd06OBuLmyOjYwVuHK+cVvDkyfnZuJ3YuN3hzZOrZIa7q8RPNDXElirPUGQaVUkSiCcBbFGepM/AuRSSaIAXe7969Gz2YOW8ndq6wKcTNxVZkTz1uiKui2ot8DuIqLvDUOydHA3FzZHTs4K3DlfMK3hyZcvvvv/2W3Ymdyw3eHJl6doirevxEc0NcieIsdYZBpRSRaALwFsVZ6gy8SxGJJmiad5VF7G7Bm47bjaXKcepxQ1xVqU3ltBBXyoAz7lPvnJlwpx8R9xRFlAPwjoJ5ehHwnqLwPjB7Wn1+6xY9f/7cO49NCN6WhOw7xJUsz1reIK5q4aucGYNKZWS1MoB3LXyVM4N3ZWS1MjTJ2yxiP/j666D4m4w7KOBJptTjhriqU7vCeSGuhIGWuEu9c3LhI26OjI4dvHW4cl7BmyOTb3/9+jWZ7w6zmD3kBd4h1MrzQFyVM4qWAuIqGurRhTCogLcPAbQTH0pyacC7GkszY2VmrkJf4B1KrjgfxFUxn6hnIa6i4sY+V3Fxgzd4exHAl70XplEi82Bms9bKrLkKfYF3KLnifBBXxXyinoW4ioobX/ZxcYM3eHsRwJe9F6aRoPrVJ59QlT2t8jyDdx6V+jaIq1KGr+jkztXRPW0jfhb+rrSpd0FEwwH1vj+g3Wmabdpvd6g3+Fh6BZsA4sqSiPOOQSUOZ3sV8LYk4ryDdxzO9iqxeZs9rcxf3VfsuOvGa/OnHjfEla2pSu/vqde+SeutPfqm+4aGNKSz7n3aau3RYeeUzkda6xl9s7NJ63vH1B/6OYe48uMklSr1zsmVE3FzZHTs4K3DlfMK3hyZmT10T6uZh9kReM9YSB5BXAXQHL7p0L2NNdo66NLZKP9b6h5czwipD9Q/vk3rrS/pZGCmtspfEFfljCRTYFCRpFnuC7zLGUmmAG9JmuW+YvGus6dVXilixZ137Tq21OOGuKpcuxMhtfEVnbyZ3PK76NHRFVdsjZ1e9Np0rXWdDrtvva4CceWFSSxR6p2TKyji5sjo2MFbhyvnFbw5MmP7H588Cd7TKs8zeOdRqW+DuKrIcNg/phutTdptvxjd/htlP+vS4cYaXWv3yJ2jGqe9SvudV15XgbjywiSWCIOKGEovR+DthUksEXiLofRyFIO32dPKLGIP3dMqryAx4s67bl1b6nFDXFWqYbvW6jY97n+Y5Rx0aL+1KK5oZIe4moFK6yj1zsnRQtwcGR07eOtw5byCN0eG6Lf37tXa0yrPM3jnUalvg7iqwnAyQ7WwSL2CuDKzU0V/pqHjDwzQBtAG0AbQBtw28ODB7+jmX9zE94PzHVnl6zt2WoirCsTHa6g26cbxKc39ABC3BStQTCepGbiW8YW449YaeIO3DwHNdmJuA5p/ys1tQemXZtzSsbr+Uo8b4sqtrcJj++u/zC1BkwcL2gvJpXoy9c7JcUPcHBkdO3jrcOW8gvciGfOIG7OQXeMF3hpUiSCuvLlONhO1m4bO5SvaiiFHjM3lnX3AgvYZixhHGFRiUJ5dA7xnLGIcgXcMyrNraPGWeMTNLMrFI624F68ka0k9bogr3/qezE6t3+nQYCGP3UR0m/aPf6ZzGtJ5v0OHO5u0dbdDb+buIS5knhogrqYoohyk3jk5CIibI6NjB28drpxX8J6RMbcDJR5xM/O4eATei0wkLBBXvhSZW3/T7AuPv9mk3YMf8PibKaD0DjCoxK0T8AZvHwJoJzNKmrcD7VXA25KQfYe4kuVZyxtmrmrhq5wZg0plZLUygHctfJUzg3dlZLUySPN+/vw5fX7r1ugBzbUCK8ksHXfJ5cROpx43xJVYVdd3BHFVn2EVD6l3Tq4siJsjo2MHbx2unFfwppGg0r4daPmDtyUh+w5xJcuzljeIq1r4KmfGoFIZWa0M4F0LX+XM4F0ZWa0Mkrx//+23ZP5ivCTjjhGvvUbqcUNc2ZpK4B3iKm4lpN45ORqImyOjYwdvHa6c18vO++XLl6NF7OYBzTFel523FmOIKy2yAX4hrgKg1ciCQaUGvICs4B0ArUYW8K4BLyCrBG8jqMztQCOwYr0k4o4Vq3ud1OOGuHJrq+FjiKu4FZB65+RoIG6OjI4dvHW4cl4vM++YtwMt/8vM2zLQeIe40qAa6BPiKhBcYDYMKoHgArOBdyC4wGzgHQguMFtd3rFvB9pi1o3b+on9nnrcEFexW0TB9SCuCuAonEq9c3JFRtwcGR07eOtw5bxeRt5N3A60/C8jb1t2zXeIK026FX1DXFUEVjM5BpWaACtmB++KwGomB++aACtmr8O7iduBtnh14rY+mnhPPW6IqyZaBXNNiCsGjJI59c7JFRtxc2R07OCtw5Xzetl4x9osFLw5Ajp2iCsdrkFeIa6CsAVnumyDeDAooYzgLQTS0w14e4ISShbCO8azA8uKFxJ3mc8Y51OPG+IqRivwvAbElScooWSpd06umIibI6NjB28drpzXy8Q7xrMDOc7Wfpl42zLHeIe4ikHZ8xoQV56ghJJhUBEC6ekGvD1BCSUDbyGQnm6q8n769GmUZweWhV817jJ/sc6nHjfEVayW4HEdiCsPSIJJUu+cXFERN0dGxw7eOlw5r5eBdwq3Ay3/y8DbljXmO8RVTNol14K4KgEkfBqDijDQEnfgXQJI+DR4CwMtcVeF92/v3aM/PnlS4jHO6Spxx4nI7yqpxw1x5VePUVJBXEXBPL1I6p1zGmjmAHFngCh/BG9lwBn3q877pNMhI65Sea0676Y4Q1w1RT7nuhBXOVAUTRhUFOHmuAbvHCiKJvBWhJvj2of369evyYzz5j2Vl0/cqcTqxpF63BBXbm01fAxxFbcCUu+cHA3EzZHRsYO3DlfO66ryNruwmxkrM3OV0mtVeTfNGOKq6Rpwrg9x5cCIcIhBJQJk5xLg7cCIcAjeESA7lyjjbdZYma0XUnuVxZ1avDae1OOGuLI1lcA7xFXcSki9c3I0EDdHRscO3jpcOa+ryLvf79OvPvmEzK8EU3utIu8UGENcpVALkxggruJWBgYV8PYhgHbiQ0kuzarxtg9lNo+5SfG1arxTYQxxlUpNEI0WOiYUjnco6JzeqEQSgrcIRm8n4O2NSiThqvFu8qHMPhWyarx9yhwjDcRVDMqe18DMlScooWQYVIRAeroBb09QQsnAWwikp5s83ma2ytwONLNXqb7y4k41Vjeu1OOGuHJrq+FjiKu4FZB65+RoIG6OjI4dvHW4cl5XhXdKu7BzrI19VXgXlbGJcxBXvtSHA+p9f0C7rbXR7bv1jS/o4YsBDW3+7PnWNu23O9QbfLQpSt8hrkoRiSbAoCKKs9QZeJciEk0A3qI4S51leae0C3tR8Nm4i9KmdC71uCGuvFrLe+q1b9LWnSd0ej4kGr6h7v09Wm/dpKPeeyIa0ln3Pm219uiwc0rnxjJ4Rt/sbNL63jH1pwqs+GIQV8V8pM+m3jm58iJujoyOHbx1uHJeV4F3aruwc6yNfRV4F5WvqXMQVx7kh/1jutG6Tofdt7PUZ1063Fija+0eXdBb6h5czwipD9Q/vk3rrS/pZHAxy1dwBHFVAEfhFAYVBagFLsG7AI7CKfBWgFrg0vK22y6ktAt7QdgQV0VwapyDuCqFNxFJG/epe8ZMQV306OjKGm0ddOnM8XfRa9O1rChzzmcPIa6yRHQ/28FQ9yry3hG3PNMij+BdREf+3DLzTn3bhbzaWmbeeeVJxQZxVVoT59Rrf0brVx7QyfNHtL8xWXO1c0BPepM1V3OzWDOH4xmvq7TfeTUzFhxBXBXAUTiFQUUBaoFL8C6Ao3AKvBWgFrg0vFPfdiEvfLSTPCr1bRBXpQxf0cmdq6NF7Ft3HtG/jhaof6RB9wHt2jVXgw7tt+wtQsfhyA5x5RBJ6hCDStzqAG/w9iGwrO3ku+/a9PmtW0lvu5DHf1l5px43xFVea5uzTcTVxld08sb55d/wlB7vbY5vBVYQV2Z2qujPNBj8gQHaANoA2sDytIH//k//YzSum3fUW7x6m/uqTuwDxFVphUwWq19pU29uXfpEdBn7O3dx+8whbgvOWKR4ZAbBZXwh7ri1Bt7gXUTArLMy2y48ePC7omTJnkP71qkaiKtSrpMF7Zy4MlstfMSC9lKMCSbAoBK3UsAbvH0ILFs7efSHR3Tw9df41Z1P5QqmSb2dQFyVVrbdw+o2Pe5/mKV2bwsWbsWQyTfzsHCEBe0LSFQNqXdOrvCImyOjYwdvHa6c12Xi7T7eZpnidtkjbpeG3DHElQ/L4Z/o5O42bd3t0JvRbgxn1O/cp93pOiwrwLZp//hnOqchnfc7dLiz6eQpvxDEVTkjyRQYVCRplvsC73JGkinAW5Lmoi+zj5V5bqDZ18q8wHuRkaYldd4QV761f96nn9pf0NZkQfrWnYf0U9/Z1Wrh8TebtHvwAx5/48u3gXSpd04OCeLmyOjYwVuHK+d1GXjbdVZmJ3b7Woa4bazuO+J2acgdQ1zJsaztCTNXtRFWcoBBpRKu2onBuzbCSg7AuxKuSonNOiuziN19gbdLQ/84dd4QV/ptwPsKEFfeqEQSpt45uUIibo6Mjh28dbhyXlPnbddZvXv3bq4Iqcc9F6zzAXE7MAQPIa4EYdZ1BXFVl2C1/BhUqvGqmxq86xKslh+8q/HySW3XWb18+XIhOXgvIFE1pM4b4kq1+qs5h7iqxqtu6tQ7J1c+xM2R0bGDtw5XzmuqvPPWWbllSDVuN8a8Y8SdR6W+DeKqPkMxDxBXYii9HGFQ8cIklgi8xVB6OQJvL0zeiex+VlwG8ObI6NhT5w1xpVPvQV4hroKwBWdKvXNyBUPcHBkdO3jrcOW8psjbrrMys1fcK8W4uVhdO+J2acgdQ1zJsaztCeKqNsJKDjCoVMJVOzF410ZYyQF4V8LFJrbrrOx+VlxC8ObI6NhT5w1xpVPvQV4hroKwBWdKvXNyBUPcHBkdO3jrcOW8psTbzFR9fusWuftZLUPcXIx59pR458XH2VKPG+KKq7kG7BBXcaGn3jk5GoibI6NjB28drpzXlHj//ttvyfz5vFKK2ydemwZxWxKy7xBXsjxreYO4qoWvcmYMKpWR1coA3rXwVc4M3pWRzWV4+vTpaNaqaJ2VmwG8XRr6x6nzhrjSbwPeV4C48kYlkjD1zskVEnFzZHTs4K3DlfOaAm+zvso8N9Cst/J9pRC3b6xuOsTt0pA7hriSY1nbE8RVbYSVHGBQqYSrdmLwro2wkgPwroRrmtjMVBlhZX4hWOUF3lVo1U+bOm+Iq/p1LOYB4koMpZej1DsnVwjEzZHRsYO3DlfOa9O8zTMDzZ5WVV9Nx101XpsecVsSsu8QV7I8a3mDuKqFr3JmDCqVkdXKAN618FXODN6VkY1EVfaBzL5ewNuXlEy61HlDXMnUs4gXiCsRjN5OUu+cXEEQN0dGxw7eOlw5r03xthuFZh/IzMWZtTcVdzaOqp8Rd1Vifukhrvw4RUkFcRUF8/QiGFSmKKIcgHcUzNOLgPcURemBWbhuxt+yjUKLHIF3ER35c6nzhriSr/NgjxBXweiCMqbeOblCIW6OjI4dvHW4cl5j87YL2M3WC3VeseOuE6ubF3G7NOSOIa7kWNb2BHFVG2ElBxhUKuGqnRi8ayOs5AC8/XCFLmDPegfvLBHdz6nzhrjSrf9K3iGuKuGqnTj1zskVEHFzZHTs4K3DlfMak7f5VaARV74bhXIxG3vMuIviqHoOcVcl5pce4sqPU5RUEFdRME8vgkFliiLKAXhHwTy9CHhPUeQe1F3AnnUK3lkiup9T5w1xpVv/lbxDXFXCVTtx6p2TKyDi5sjo2MFbh7M2AnQAACAASURBVCvnNQZviQXs2fhjxJ29psRnxC1BcdEHxNUik8YsEFdx0WNQAW8fAmgnPpTk0mjztgvYq+7AXlZC7bjLrh96HnGHkivOB3FVzCfqWYirqLixRiIubvAGby8Cml/2RlhJLWDPFkYz7uy1JD8jbkmaM18QVzMWjR9BXMWtAgwq4O1DAO3Eh5JcGk3edgG7XLQzT5pxz64if4S45ZkajxBXXlwvaND5crTJnBFAs7/P6Kh3PvYwHFDv+wPanZ7fpv12h3qDj15XMIkgrrxRiSTEoCKC0dsJeHujEkkI3vMYTzod+vzWLZFfBs57Hn8C7zwqerbUeUNcedX9W+oeXKf1vWPqD/MyDOmse5+2Wnt02DklI7eGg2f0zc5mQZ5FPxBXi0w0Lal3Tq7siJsjo2MHbx2unFcN3i9fvqRfffIJmYXsWi+NuLVidf0ibpeG3DHElQ/L4Sk93tukrYMuneWmzxNfH6h/fJvWW1/SyeAiN1fWCHGVJaL7GYOKLt+sd/DOEtH9DN5jvkZQGWFlBJbmC7w16S76Tp03xNVinS1azrp0uHGV9juvFs8Zy0WPjq6sLYivi16brrWu02H3bX6+jBXiKgNE+WPqnZMrPuLmyOjYwVuHK+dVkrdZwG5uBdZ9tA0Xq2uXjNv1q32MuHUIQ1x5cB2LpG36yzuf05ZdU7VzQE96AxrdJRyJrzW61u6RO0c17B/TjVaBKMtcG+IqA0T5IwYVZcAZ9+CdAaL88bLz1vxlYF7VXXbeeUw0banzhrgqrX17e2+b9o9/Hq2nIhrS+ekT2t+4SUe990SDDu23FsXV2A5xVYq4oQSpd04OC+LmyOjYwVuHK+dVirfmLwPzYpeKO8+3pg1x69CFuArm+opO7lwdL1h/7S+uzOxU0Z9p6PgDA7QBtAG0gfA28ODB7+jTX39K//wvP2I8XeHvlOCv7wgZIa6CIU/E1ZU29d6ZNVmLM1e4LRgMN0pG8+W1jC/EHbfWwHu5eNtnBmr+MjCPCNpJHhU9W+q8Ia6C694RVx+woD0YY4MZU++cHBrEzZHRsYO3DlfOax3eGs8M5OLM2uvEnfUV8zPi1qENcVXKdbLNwsZ96p45m1zNbc9QtBXDbXrc/1B6FZMAC9q9MIklwqAihtLLEXh7YRJLdNl42y0XpJ8Z6Fshl423LxetdKnz1hdXIxHyG+/tCKpUxPi22xqtZ4VPFSelaYd03ntIuy13QftHGnQf0O7GV3TyxuzAbjcRtWmGdN7v0OHOJm3d7dAbR5MVXQ7iqoiO/LnUOydXYsTNkdGxg7cOV85rCG/7y8A/PnnCuVW3h8StHpTHBRC3B6SAJGHiarKvk7swm9tgcySAVMTPe+q1b9L6bz6j3Y1NunF8Ot4WIQBCeZaPNOh16OjO9nQx+tadh/RT39lSdOHxN5u0e/ADHn9TDrexFBhU4qIHb/D2IVC1nVhhZX4d2OSratxNxupeG3G7NOSOw8TV6Pr2dtldenzqiIy52CYzOuxjY+YSV/sw2ltqk278wz/RP+5Ve8xMtQvFS42Zq3iszZUwqIC3DwG0Ex9Kcmmq8o695QJX0qpxc35i2xG3DvFwcTW35ogLzgiw3zCzSvZhyHt0+A9/Q/sbky0KNr6ghy9O6fTZw5lt5z6duLNE09twZvfzV5PHzPivbeKibdoOcRW3BjCogLcPAbQTH0pyaarwtsLKzF41/aoSd9OxutdH3C4NueNgcTVe71TyaJfR7BIneqy4WqP1nQfUHXwkOn9BR+Zhx6012rrziP518JF5ALKdNRsvMh/Hon1rUA465wniiiOjY8egosOV8wreHBkd+6rzbmrLBa62Vp03V+6m7KnzDhRXdtfy4ocSF6+3suLKFWjWr2s7p177s/kHIE8eNzNd5zWZRVvXuP0YseVAXEWEjduCcWGDN3h7EvD50kxNWJmi+cTtiSBqMsStgztQXDm7k7O/hBsLpakAWojfiqvP6Kh3Pjlrba5oy4qrj/Sm8xVttdwZsTxRtnDB5A0QV3GrCIMKePsQQDvxoSSXpoy33XLh5cuXchcV8FQWt8AlVFwgbhWsFCau7GLyol/olW7BYIVURXFlZ6mYx8jwYk4HoKRXiCtJmuW+MKiUM5JMAd6SNMt9rSJvK6ya2suqiPoq8i4qb9PnUucdIK7snk7uzFEO5sL1ViZ9mLji11fNr8PKiSh5E8RV3CpKvXNyNBA3R0bHDt46XDmvHG+zaP3zW7fopNPhsjZq5+JuNCiPiyNuD0gBSQLElY+I8dmCIURcnY9/GTjdvNMtsRV97not93z6xxBXcesIgwp4+xBAO/GhJJcmj3cqe1kVlTIv7qL0qZxD3Do1UVFc2d3K16j49lvRFgy2IAHi6vXP9Hhvk7+2XeheYVd0G00K7xBXcWsBgwp4+xBAO/GhJJcmy3sZhJUpfTZuOSK6nhC3Dl9/cZWzK/v6lTb1LnICK11vZfJUFVd36XHnO9ptFc1MTXZtn1vsnhNfoiaIq7gVg0EFvH0IoJ34UJJLk+Wd0l5WRaXMxl2UNqVziFunNvzFlc714dUhAHHlwIhwiEElAmTnEuDtwIhwuAq8l0VYmepcBd4RmqXYJVLnDXElVtX1HUFc1WdYxUPqnZMrC+LmyOjYwVuHK+fV8jYPYTYL2FPYfZ2L1bXbuF3bMhwjbp1agrjS4RrkFeIqCFtwJgwqweiCMoJ3ELbgTMvMO8VNQssqYpl5l5UtxfOp84a4SqjVQFzFrYzUOydHA3FzZHTs4K3DlfP6d3/3B/rVJ5+Q2dNqmV5oJ3FrK3XeEFdx20Ph1SCuCvGIn0y9c3IFRtwcGR07eOtwzfNqZqx+ee0XSyesTFnQTvJqVM+WOm+IK726r+wZ4qoysloZUu+cXOEQN0dGxw7eOlyzXs1MlRkDzczVMr7QTuLWWuq8Ia7itofCq0FcFeIRP5l65+QKjLg5Mjp28Nbh6np1H2sD3i4Z/WPw1mEMcaXDNcgrxFUQtuBMGFSC0QVlBO8gbMGZloW3K6xMYZcl7mzFIO4sEd3PqfOGuNKt/0reIa4q4aqdOPXOyRUQcXNkdOzgrcPVeM0KK2MDbz3eeZ7BO49KfRvEVX2GYh4grsRQejnCoOKFSSwReIuh9HKUOm8rrMx+Vu4r9bjdWN1jxO3S0D9OnTfElX4b8L4CxJU3KpGEqXdOrpCImyOjYwdvea5FzwsEb3neRR7Bu4hO+DmIq3B24jkhrsSRFjrEoFKIR/wkeIsjLXSYKu8iYWUKlGrchbARdxke8fOptxOIK/EqD3cIcRXOLiRn6p2TKxPi5sjo2MFbjmuZsDJXAm853j6ewNuHUvU0EFfVmanlgLhSQ5vrGINKLhY1I3iroc11nBpvH2FlCpJa3Llwc4yIOweKoil13hBXlSt/SOe9h7Tbukr7nVez3MMB9b4/oN3W2mgjvPXWNu23O9QbfJylKTmCuCoBJHw69c7JFRdxc2R07OBdn6uvsDJXAu/6vKt4AO8qtPzTQlz5sxqnPH9BRzubtD4nroZ01r1PW609Ouyc0jkRDQfP6BuTbu+Y+kO/i0Bc+XGSSoVBRYqknx/w9uMklSoV3lWElSl7KnFXrQfEXZVYvfSp84a4qlS/76nXvjmZmXJnrt5S9+B6Rkh9oP7xbVpvfUkngwuvq0BceWESS5R65+QKirg5Mjp28A7nWlVYmSuBdzjvkJzgHUKtPA/EVTmjSQp7O/Amfdv+a7rmzlxd9OjoyhptHXTpzPF30WvTtdZ1Ouy+daz8IcQVz0bjDAYVDaq8T/Dm2WicaZp3iLAyHJqOO7QuEHcoubB8qfOGuPKt19HtwKu0235B/3ckmpyZq7MuHW6s0bV2j9w5qmH/mG64IqzkWhBXJYCET6feObniIm6OjI4dvKtzDRVW5krgXZ13nRzgXYcenxfiimfjnJncDtx5SL3zIY1npBxxNejQfmtRXNHI7qRzPOYdQlzlUdGzYVDRY5vnGbzzqOjZmuJdR1gZGk3FXbcmEHddgtXyp84b4qq0Pme3A49670ep64grI6CK/kyDwR8YoA2gDSxjG/jnf/mRbv7FTfqrv/prjGMYy9XbQOnXd4MJIK7K4Du3A82vAM1rQVzhtuCEzHK9mS+vZXwh7ri1Bt5+vOvOWNmrgLclEecdvHU4Q1yVcB0LqYLZpjsdGmBBewnFNE9jUIlbL+C9urylhJUhhHayuu1EsmSptxOIq4DaXpi5oqKtGG7T4/4Hr6tgzZUXJrFEqXdOrqCImyOjYwfvYq6SwspcCbyLeUufBW9pomN/EFcBXBfFld1EdJv2j3+mcxrSeb9DhzubtHW3Q2+wiWgAZf0sGFT0GbtXAG+Xhv5xDN7SwspQiRG3Bn3ErUGV95k6b4grvu7YM4viarQle+bxN5u0e/ADHn/DUmz+ROqdkyOEuDkyOnbwzuf67t07+u29e/ToD4/yEwRawTsQXGA28A4EV5IN4qoEUMzTuC0Ykzb+Q45LG7xXiffr16/pV598Ii6sDCN82cdtKeCtwxviSodrkFeIqyBswZkwqASjC8oI3kHYgjNp8bbC6o9PngTHVpRRK+6ia0qcQ9wSFP19pM4b4sq/LtVTQlypI567QOqdcy5Y5wPidmBEOATvGWQrrJ4/fz4zCh+BtzDQEnfgXQIo8DTEVSA4jWwQVxpUeZ8YVHg2GmfAW4Mq71OadwxhZUojHTdPSPYM4pblWeYtdd4QV2U1GPE8xFVE2BjE48IG76XmbWaqzBorzRkrCyj1L00bZ/YdcWeJ6H5OnTfElW79V/IOcVUJV+3EqXdOroCImyOjY7/svGMKK1ODl523TivmvYI3z6bOGYirOvSE80JcCQMtcYdBpQSQ8GnwFgZa4k6CtxVW5pZgrJdE3LFida+DuF0a+sep84a40m8D3leAuPJGJZIw9c7JFRJxc2R07JeVt/k1oLkVGFNYmRq8rLx1Wm+5V/AuZxSSAuIqhJpSHogrJbCMWwwqDBglM3grgWXc1uFtNgb9/Nat6MLKFKVO3AyKKGbEHQXz9CKp84a4mlZV8wcQV3HrIPXOydFA3BwZHftl4m0eZ2OEldl53Rw38bpMvJvgm70meGeJyHyGuJLhKOIF4koEo7cTDCreqEQSgrcIRm8nVXnb5wQ2KaxM4arG7Q1EOSHiVgaccZ86b4irTIU1+RHiKi791DsnRwNxc2R07JeBtxVWZtaqqRkrW3uXgbctawrv4K1TCxBXOlyDvEJcBWELzoRBJRhdUEbwDsIWnMmXt90cVPoBzKGB+8Yd6l8rH+LWIpvvN3XeEFf59daIFeIqLvbUOydHA3FzZHTsq8zbCqunT5/qwAvwusq8A3CoZwFvHcQQVzpcg7xCXAVhC86EQSUYXVBG8A7CFpypjLfZw8qMOTF2Xa9SiLK4q/iKmRZxx6Sd/to8iKu47aHwahBXhXjET2IwFEda6BC8C/GInyzibWaqzB5W/X5f/Lp1HRbFXde3Zn7ErUl30XfqvCGuFuusMQvEVVz0qXdOjgbi5sjo2FeNt1lb1cTmoL61s2q8fcvdVDrw1iEPcaXDNcgrxFUQtuBMGFSC0QVlBO8gbMGZsrzNrwB//+23je5h5VOYbNw+eVJIg7jj1kLqvCGu4raHwqtBXBXiET+ZeufkCoy4OTI69lXgbbdaMOKq6a0WymppFXiXlTGl8+CtUxsQVzpcg7xCXAVhC86EQSUYXVBG8A7CFpzJ8ra/CExlq4WyAtm4y9Kldh5xx62R1HlDXMVtD4VXg7gqxCN+MvXOyRUYcXNkdOzLzNv8EtCsr0rtF4FFNbXMvIvKleo58NapGYgrHa5BXiGugrAFZ8KgEowuKCN4B2ELzvTdd+2RsHr58mWwjyYyop3EpQ7eOrwhrnS4BnmFuArCFpwJg0owuqCM4B2ELSiTuQX46a8/JXNLcNleaCdxawy8dXhDXOlwDfIKcRWELTgTBpVgdEEZwTsIW6VMduG6efjyP//Lj5XyppIY7SRuTYC3Dm+IKy+uQzrv/0hHd7ZHOxqvt7Zpv92h3uDjLPdwQL3vD2i3tcanmaXOPYK4ysWiZsSgooY21zF452IRM5pZqs9v3SK7cB28xdB6OQJvL0xiiVLnDXHlUdXDNx26t7FJuwcd6p8PaTh4Rt/sbNL6zkPqnQ+JaEhn3fu01dqjw84pnRuLTbN3TH2TxOMFceUBSTBJ6p2TKyri5sjo2JeBt1247j4jcBnizqsxxJ1HRc8G3jpsIa5KuX6g/vFtWm/dpsf9D5PUFzTofEnrrc/oqGek1FvqHlyn9TkhZfN9SSeDi9KrmAQQV16YxBJhUBFD6eUIvL0wVU500unkLlwH78ooa2UA71r4KmdOnTfEVeUqNRky4uqiR0dX1mjroEtnjr+LXpuuta7TYfetY+UPIa54NhpnUu+cXJkRN0dGx54qb3fH9byF66nGXVZLiLuMkOx58Jblab1BXFkS3u9m/VWHDnc2aetuh96YW35nXTrcWKNr7R65c1TD/jHdaF2l/c4rL+8QV16YxBJhUBFD6eUIvL0weSUyYsosWi/acR28vVCKJQJvMZRejlLnDXHlVY2TRMNTery3OV6wvvEFPXwxoNFyqkGH9luL4opG9nlxZQRU0Z9pMPgDA7QBtAGuDfyX//qP9Mtrv6AHD36HsQLj5aVuA1W+vmOnhbgKIv6RBt0HtNvapnudP9GwgrgquhxmroroyJ8zX17L+ELccWstJd7c+qo8IinFnRcfZ0PcHBkdO3jrcIW4CuVqZ7HMIvb3uC0YirHJfBhU4tIH73DeZeur8jyDdx4VPRt467HN85w6b4irvFrzsr2ikztXaf1Km3ofsKDdC1liiVLvnBwuxM2R0bE3zdvuX1W0viqv5E3HnReTjw1x+1CSSwPecixdTxBXLo3c48k2Cxv3qXvmbFg1mbkaL2ov2orB3cIh9wJTI24LTlFEOcCgEgXz9CLgPUXhfZC3f5VvZvD2JSWTDrxlOPp6SZ03xFVpTQ7pvPdwtL5q//jn0QahRGfU79yn3dZNOuq9dzYR3aZxmpxfFJZeB/tceSASTZJ65+QKi7g5Mjr2pnibndZ/9ckn1O/3gwrWVNxBwTqZELcDI8IheOtAhrjy4vqRBr2O8/ibNdq685B+6ju7Wi08/sbs6P7D/CNySq6FmasSQMKnMagIAy1xB94lgCan3717N9pmwWy1YNZahb7AO5RcWD7wDuMWmit13hBXoTWrkA/iSgFqgcvUOycXOuLmyOjYY/J++fLlaLbqj0+e1C5MzLhrB+s4QNwOjAiH4K0DGeJKh2uQV4irIGzBmTCoBKMLygjexdiMoDK3AY3AkniBtwRFfx/g7c9KImXqvCGuJGpZyAfElRBITzepd06uGIibI6Nj1+bt3gY0x1Iv7bil4sz6QdxZIrqfwVuHL8SVDtcgrxBXQdiCM2FQCUYXlBG8F7FJ3gbMegfvLBHdz+CtyzfrPXXeEFfZGmvwM8RVXPipd06OBuLmyOjYNXibherStwGzpdeIO3sNjc+IW4Mq7xO8eTZ1zkBc1aEnnBfiShhoiTsMKiWAhE+D9xiofejywddfk+RtwGx1gXeWiO5n8Nblm/WeOm+Iq2yNNfgZ4iou/NQ7J0cDcXNkdOySvJ8+fTpatG6eEaj9koxbO1bXP+J2aegfg7cOY4grHa5BXiGugrAFZ8KgEowuKONl5m2fDfj5rVvBm4JWhX6ZeVdlJZEevCUo+vtInTfElX9dqqeEuFJHPHeB1DvnXLDOB8TtwIhwWJe32WHdiKqqzwasW7S6cde9fmh+xB1KLiwfeIdxK8sFcVVGKOJ5iKuIsIkIgwp4+xCo007sonXzjMDYrzpxx47VvR7idmnoH4O3DmOIKx2uQV4hroKwBWfCoBKMLijjZeJtF62bR9hoLlovqojLxLuIQ6xz4B2L9Pg6qfOGuIrbHgqvBnFViEf8ZOqdkysw4ubI6Nir8jaL1k1fjrFovajEVeMu8hXzHOKOSRsz+Fq0Ia60yAb4hbgKgFYjCwbxGvACsq46bzNDZbZXMOurzMxV069V59003+z1wTtLRPdz6rwhrnTrv5J3iKtKuGonTr1zcgVE3BwZHbsPb7OmyjwX0KyxMr8MTOHlE3cKcWZjQNxZIrqfwVuHL8SVDtcgrxBXQdiCM2FQCUYXlHEVeTexxYIv/FXk7Vv2JtKBd1zqqfOGuIrbHgqvBnFViEf8ZOqdkysw4ubI6Ng53va5gI/+8CiZ2SqXABe3mybFY8Qdt1bAW4c3xJUO1yCvEFdB2IIzYVAJRheUcVV429kqcxvQCKxUX6vCO1W+2bjAO0tE93PqvCGudOu/kneIq0q4aidOvXNyBUTcHBkdu8vbzlbF3hA0pGRu3CH5m8qDuOOSB28d3hBXOlyDvEJcBWELzoRBJRhdUMZl5r0ss1VuxSwzb7ccy3IM3nFrKnXeEFdx20Ph1SCuCvGIn0y9c3IFRtwcGR37d9+1k/sloE9J0U58KMmlAW85lj6eUucNceVTi5HSQFxFAj25TOqdk6OBuDkysna7b9Wnv/402sOWJUuAdiJJs9wXeJczkkyROm+IK8narukL4qomwIrZU++cXHEQN0dGzm52V7f7Vv3zv/wo5ziiJ7STiLDxrNK4sJeAN8RV9CbBXxDiimejcQZfPhpUeZ/LwNt9JqDdZX0Z4s6jjrjzqOjZwFuPbZ7n1HlDXOXVWkM2iKu44FPvnBwNxM2RCbebBetmd3UzW5V9JiB4h3MNyQneIdTC84B3OLuinBBXRXSm5z7SoPcDHe5sjh7IakTQ1p02nfQGNLRphgPqfX9Au621SZpt2m93qDf4aFOUvkNclSISTYBBRRRnqbNUeZvtFczzAM1zAc06q+wr1bizcWY/I+4sEd3P4K3LN+s9dd4QV9kaW/g8pPPeQ9ptbdP+3z6ngVFT56d0crBH662bdNR7T0RDOuvep63WHh12TuncWAbP6BsjxvaOqT9VYAvO5wwQV3M41D+k3jk5AIibI1PNbhesl20GCt7VuNZNDd51CVbLD97VePmmhrgqJfWWugfXaf1Km3oXTuKzLh1urNHWQZfOaJJmTkh9oP7xbVpvfUknAzej4yNzCHGVAaL8EYOKMuCM+5R4uwvWzS3BoldKcRfFmT2HuLNEdD+Dty7frPfUeUNcZWvM9/NFj46urNH6nQ4NJsdjoTVzcNFr07XWdTrsvp0ZC44grgrgKJxKvXNyRUbcHJlye7/fn94CtAvWy3KBdxkh2fPgLcuzzBt4lxEKOw9xFcaNhv1jutFao2vtHl1MZrFGx46/cZqrtN955Vj5Q4grno3GGQwqGlR5n03yNrcAzSNrzC3A58+f80HmnGky7pxwvE2I2xuVSELwFsHo7SR13hBX3lXpJnxPvfZNWm/dpsf9D0SDDu1boeUmG9nnxZURUEV/psHgDwzQBuTawIMHv6NfXvsFHRz8ZzJ7VoGtHFuwBMsm24D7dZvaMcRV5RqZLXC/1/nT+NeCFcRV0eUwc1VER/6cGRSW8YW4/WrN/RWg7y3APM/gnUdFzwbeemzzPIN3HpX6NoirSgyHdH76hPY3Nmm3/WL0q8BRdtwWrEQxlcQYVOLWRCze9leAZnuFqrcA84jEijvv2nVsiLsOvep5wbs6szo5UucNceVdux9p8OLRWFjdfzbeksHmxYJ2S2Kp3lPvnBxMxJ1Pxm4EamaAza8By34FmO9l0Qrei0w0LeCtSXfRN3gvMpGwQFx5UTyj0+O7tNXapN2ssBrlL9qKYbIuy+M6uC3oAUkwCQYVQZgerjR5P336dLRY3Sxaz9sI1CM8Nolm3OxFBU4gbgGIFVyAdwVYAklT5w1xVVrJH+lN5yvaMruy3+3Qm9wNQe0motu0f/wzndOQzvud0Y7ufJ7FC0NcLTLRtKTeObmyI+4ZGbuu6rf37pHZZkHjBd4aVHmf4M2z0TgD3hpUiSCuyrja/ay4X/nZzUUXHn+zSbsHP+DxN2V8GzyPQSUufEneRkiZx9VIrasqIiEZd9F1pM8hbmmixf7Au5iP9NnUeUNcSdd4DX+YuaoBLyBr6p2TK9Jljtvc8nv0h0fTByxLraviWBv7ZeZdxEXrHHhrkc33C975XOpaIa7qEhTMD3ElCNPDFQYVD0iCSerwNiLKLFI3fcSIqxiiyha9TtzWRxPviDsudfAGb5cAxJVLo+FjiKu4FYDBMH3eVlSZndU1Fqv7EEA78aEklwa85Vj6eAJvH0rV00BcVWemlgPiSg1trmMMKrlY1IxVeZs9qsyaKrO2Smuxuk9hq8bt4zNGGsQdg/LsGuA9YxHjKHXeEFcxWoHnNSCuPEEJJUu9c3LFXPW4rajS/AUgxzbPvuq888rcpA2849IHbx3eEFc6XIO8QlwFYQvOhEElGF1QxjLedluFGL8ArFKAsrir+IqZFnHHpI0fPsSlnT5viKvYLaLgehBXBXAUTuHLRwFqgUuOd8xtFQrCY09xcbMZEjmBuONWBHiDt0sA4sql0fAxxFXcCsBg2Czv1EWVpYN2YknEeQfvOJztVcDbkpB9h7iS5VnLG8RVLXyVM2NQqYysVgbL24oq8wtA89ia1F827tTjzMaHuLNEdD+Dty7frPfUeUNcZWuswc8QV3Hhp945ORrLGvf3T/7b6Jd/RlRJPliZ4yRlX1beiFuqBfj5AW8/TlKpUucNcSVV0wJ+IK4EIFZwkXrn5IqybHHbmapPf/0pmV8CxtwAlGNYxb5svG3ZELclEecdvONwtldJnTfEla2pBN4hruJWQuqdk6OxLHEbIWW2U7C//luWuLPcEXeWiO5n8Nblm/UO3lkiMp8hrmQ4iniBuBLB6O0Eg4o3qkoJ7T5VVlTZzOBtScR5B+84nO1VwNuSiPOeOm+IqzjtwOsqLxf4xAAAGjVJREFUEFdemMQSpd45uYKmGLe51ceJKluOFOO2sRW9I+4iOvLnwFueaZFH8C6iE34O4iqcnXhOiCtxpIUOMagU4vE66T77r+wxNeDthVQsEXiLofRyBN5emMQSpc4b4kqsqus7griqz7CKh9Q7J1eWFOJ+9+4dPfrDI7IPVDaL1steKcRdFmPeecSdR0XPBt56bPM8g3celfo2iKv6DMU8QFyJofRyhEHFC9NcIiOijKgybdW8G5Hl+wJvX1Iy6cBbhqOvF/D2JSWTLnXeEFcy9SziBeJKBKO3k9Q7J1eQJuI266nMbb86e1Q1ETfHsIodcVehVT8teNdnWMUDeFeh5Z8W4sqflXpKiCt1xHMXwKAyh2Phg1lPZXZQN7/6s7/8q7NHFXgvIFY1gLcq3gXn4L2ARNWQOm+IK9Xqr+Yc4qoar7qpU++cXPm043bXU5nZqpcvX3KhVLJrx10pmAqJEXcFWAJJwVsAYgUX4F0BVoWkEFcVYGknhbjSJjzvH4PKPA8jon7/7bejW39V11PNe8r/BN75XLSs4K1FNt8veOdz0bKmzhviSqvmA/xCXAVAq5El9c7JFU0y7uytP3MbsM6tPy5mY5eMu+g60ucQtzTRYn/gXcxH+ix4SxMd+4O40uEa5BXiKghbcKbLPKi8fv16upWC5K2/osq4zLyLuGidA28tsvl+wTufi5Y1dd4QV1o1H+AX4ioAWo0sqXdOrmihcZsZKfu8P/Orvz8+eVJpKwUuHl97aNy+/rXSIW4tsvl+wTufi5YVvHXIQlzpcA3yCnEVhC0402UZVMwCdSOkjKAyD1I2AquJ12Xh3QTbvGuCdx4VPRt467HN85w6b4irvFortL2nXvsmrd/p0MBNNxxQ7/sD2m2tjTZYXG9t0367Q73BRzdV4THEVSEe8ZOpd06uwD5xZ2epzAJ1cyuwyZdP3E3Gx10bcXNkdOzgrcOV8wreHJl6doirSvzO6PT4Lm0ZATUnroZ01r1PW609Ouyc0jkRDQfP6JudTVrfO6b+0O8iEFd+nKRSreKg4q6lsrNUWgvUq9bDKvKuyiBmevCOSRs/2IhLO33eEFeeLWI4eEFPDm7T/t8/osMrWXH1lroH1zNC6gP1j2/TeutLOhlceF0F4soLk1iiVfnyMeLJ/MrPiKkm1lL5Vsiq8PYtb9PpwDtuDYA3eLsEIK5cGuzxKzq5s02795/R4GOPjrLi6mJs2zro0pnj46LXpmut63TYfetY+UOIK56NxpllHwztvlSm3Zj9qaQ2+9RgbXwuO28tLlp+wVuLbL5f8M7nomVNnTfElVfNn1G/92+j2300EVJztwXPunS4sUbX2j1y56iG/WO60bpK+51X06uYL8KiP9Ng8AcGXBv47//0P+jg4D/TL6/9gj799af03XdtOvmf/wttBv0GbQBt4NK1gekXa4IHEFdVKyVPXA06tN9aFFc0ss+Lq6LLYeaqiI78udT/87ElNr/2c2/7GXHV9OJ0G1uV92XhnS0T4s4S0f0M3rp8s97BO0tE5jPEVVWOEFcLxNA5F5DUNthf+5kNPrO3/cC7Nt5KDsC7Eq7aicG7NsJKDsC7Ei7vxBBX3qgmCfPEVYXbgkWXw8xVER35cykOKu46KiOszJ5U2V/7pRi3T+0gbh9KcmnAW46ljyfw9qEklyZ13hBXVes6T1xNbFjQXhVms+lT6ZxGUJl9qOwmn+YWoLkVyL1SiZuLj7Mjbo6Mjh28dbhyXsGbI6NjT503xFXVes8TV1S0FcNtetz/4HUVzFx5YRJL1GTndAXV57dujdZUFQkqt9BNxu3GUfUYcVclVi89eNfjVzU3eFclVi996rwhrqrWb664spuIbtP+8c90TkM673focGeTtu526A02Ea1KOUr62J0zK6jMI2lCFqbHjluqMhC3FEk/P+Dtx0kqFXhLkfTzkzpviCu/epylyhVXoy3ZM4+/2aTdgx/w+JsZueSOYnROKUHlwosRt3s9qWPELUXSzw94+3GSSgXeUiT9/KTOG+LKrx6jpMJtwSiYpxfR6Jxm8bkrqMyu6aEzVNNAMwcacWcuofIRcatgZZ2CN4tG5QR4q2BlnabOG+KKrbr4JyCu4jKX6px22wSzS7qpQyOoyhal1ympVNx1YgjJi7hDqIXnAe9wdiE5wTuEWnie1HlDXIXXrXhOiCtxpIUO63ROd2NPU29GWGkKKrcgdeJ2/cQ+RtxxiYM3ePsQQDvxoVQ9DcRVdWZqOSCu1NDmOq46qPT7/dEtPvPrPrNtgtk+IW8fqtyLCRqrxi146VquEHctfJUzg3dlZLUygHctfJUzp84b4qpyleplgLjSY5vnuaxz2tt9dg8qI6rM+imzpqrJV1ncTcZWdG3EXURH/hx4yzMt8gjeRXTkz6XOG+JKvs6DPUJcBaMLypjXOc3WCOb2nn3sjHk3n0O2TAgKyiNTXtwe2RpPgrjjVgF4g7cPAbQTH0rV00BcVWemlgPiSg1trmMzqLi/7mv6dl9ukDlGDIY5UBRN4K0IN8c1eOdAUTSBtw5ciCsdrkFeIa6CsFXOZGahTjod+g//z/87/XWf+ZzS7FRRoTAYFtGRPwfe8kyLPIJ3ER35c+Atz9R4hLjS4RrkFeIqCFtpJvPLPrPw3PyizyxENzNUZh3Vf/mv/7jwUORSZwkkwGAYtxLAG7x9CKCd+FCSS5M6b4grubqu7QniqjbCkQN7q88sPjdCynC1WyW4s1Opd06OBuLmyOjYwVuHK+cVvDkyOnbw1uEKcaXDNcgrxFUQtlEms02CubVnNvA0HM27+Wzs3AuDCkdGxw7eOlw5r+DNkdGxg7cOV85r6rwhrriaa8AOceUP3Yop+6s++5gZs02CmbnyeaXeObkyIG6OjI4dvHW4cl7BmyOjYwdvHa4QVzpcg7xCXPHYsmLKrpuqs4knBhWet8YZ8NagyvsEb56Nxhnw1qDK+0ydN8QVX3fRz0BczZAXiSmzQF3ilXrn5MqIuDkyOnbw1uHKeQVvjoyOHbx1uEJc6XAN8nqZxVUMMZWtFAwqWSK6n8Fbl2/WO3hnieh+Bm9dvlnvqfOGuMrWWIOfL4u4sr/mMwvOs2umzG0+qZmpsqpMvXNy8SNujoyOHbx1uHJewZsjo2MHbx2uEFc6XIO8rqq4svtMma0R3F/z2ef0+S5AD4JakAmDSgEchVPgrQC1wCV4F8BROAXeClALXKbOG+KqoPJin1oVcWX2kjLP4zMbddp9pswMVdnWCLF5p945OR6ImyOjYwdvHa6cV/DmyOjYwVuHK8SVDtcgr8sorsys0/dP/ttIOBkBZXdAz9u0MwiKYiYMKopwc1yDdw4URRN4K8LNcQ3eOVAUTanzhrhSrPyqrpdBXOXd4rv5FzfJ3OKLuV6qKtu89Kl3zryYjQ1xc2R07OCtw5XzCt4cGR07eOtwhbjS4RrkNUVxZX/FZ5/LZ2amsrf40DmDqjs4E3gHowvKCN5B2IIzgXcwuqCM4B2ErTQTxFUpongJmhZXZlbK7HCeXXhu1k6ZWSn3uXwuFXROl4b+MXjrM3avAN4uDf1j8NZn7F4BvF0acscQV3Isa3uKLa7MrJRZeG5mpbILz/EYmdrVqeYAg6Ea2lzH4J2LRc0I3mpocx2Ddy6W2kaIq9oI5Rxoiit3VsruLWUfIWMEFjcr5VM6dE4fSnJpwFuOpY8n8PahJJcGvOVY+ngCbx9K1dNAXFVnlp9jOKDe9we021ojI5LWW9u03+5Qb/AxP32OVVJcSc1K5YS5YELnXECiagBvVbwLzsF7AYmqAbxV8S44X1XeZusfs6TFTCw08YK4EqE+pLPufdpq7dFh55TOiWg4eEbf7GzS+t4x9Yd+FwkVV5qzUj6Rr2rn9Cl7E2nAOy518AZvHwJoJz6U5NKU8Tbfi0Zcme/VJkQWxJVIXb+l7sH1jJD6QP3j27Te+pJOBhdeV/EVV0WbdFZZK+UVlEeiskbu4aKRJIg7LnbwBm8fAmgnPpTk0qw676ZEFsSVRBu96NHRlTXaOujSmePvotema63rdNh961j5wzxxZTbptNshuGulUtqkc9U7J19jzZwB77jcwRu8fQignfhQkktTlXdskQVxJVHXZ1063Fija+0euXNUw/4x3Whdpf3Oq+lVjIDCHxigDaANoA2gDaANNNsG6vyQa/qlzhxAXDFgKpkHHdpvLYorGtnnxVWRX9PR3JdR2svwysa9DDGbGBF33JoCb/D2IYB24kNJLs1l4m3uAtnHtJkF7+bOkNYL4kqCrJK4kggtho/L1Dlj8Cy7BniXEZI9D96yPMu8gXcZIdnzl4F3TFFlawfiypKo817htmDRZS5DIy8qf+xz4B2XOHiDtw8BtBMfSnJpVpl3E6LK1gzElSVR511xQXudsGLlXeXOGYthleuAdxVa9dOCd32GVTyAdxVa9dOuKm/zGDfzLFzt239cDUBccWQq2Yu2YrhNj/sfvLytaiP3KnwDicA7LnTwBm8fAmgnPpTk0qwqb7NmWXNNVVkNQFyVEfI6bzcR3ab945/pnIZ03u/Q4c4mbd3t0BvlTUS9QlRMtKqdUxFZLdfgXQtf5czgXRlZrQzgXQtf5czgXRmZVwaIKy9MHokWHn+zSbsHPzT2+BuPiMWSoHOKofRyBN5emMQSgbcYSi9H4O2FSSwReIuhnHMEcTWHAx9AAARAAARAAARAoB4BiKt6/JAbBEAABEAABEAABOYIQFzN4cAHEAABEAABEAABEKhHAOKqHj/kBgEQAAEQAAEQAIE5AhBXczjwAQRAAARAAARAAATqEYC4qscPuUEABEAABEAABEBgjgDE1RyOBj4sbOGwTfvtTqUtHPSi/kiD3g+j/brMz3XN39adNp30BlS4ddfkWYs2j32/1u7RhV6wvOfzF3S0s037nVd8GnMmmbp4T732TVq/06FBYcQXNOh8OaoXy3j8/hkd9c4Lc0qcHA5e0JODvdn1N76go06PBgWNIySPRKzzPkLadbOsp/Gf9+mn9he0VaU/JtGuzd5/P9LRne1Je/EZ5xJhPoVvDiZ9s/UlnQwKRrMkmLuBD+m895B2W1fLx8HGx++wek9jbJkxh7iasWjgyG4+ukeHnVMyX4fDwTP6ZmeT1veOqV/wJRUl2NEzE81+XR3qnw+Jhm+oe998mRbtOm/LVJQmSvTji5z/TI9HA3rZoGLjbrouzuj0+O74y7NUXOU9GSAS25Fg3aStO4/oXwcfieiM+p37tNvapN32i1FbXoxkEu/OfTrpnxHRRxp0H4zy3Dg+LRbsi84CLfZLZpv2//b5WAien9LJSCTepKPee8Zvg6xtRMM/0cndbVq3/Kb9sSjuNNr18E2H7m3MxpLpOLfzkHpmbMl9JcB8Li7bdsw/mkXiKg3mc6FP+ut6qbiysTc5fofUewpjyxxxgria5xH5U14j+kD949slnTdGmPmdbNg/phuFHXQS/8Z96p5xg2aM+CezE3tf0t//w3+ka4Uxm3iar4vxf163af/vH9HhlbXymavhKT3e26Stgy4ZqRLvZdtGdoZswpCr+4lYnxNSkzKUz9JJlW4S45U29dyJh8nD11mWjbGelXvc9zZpjt9kloGfFW6+XRPZMc39wrazE9k2NCsvJcDciYZoKlDKxFUKzN3I7Wybibvsn8wExu+Qek9ibHGZE8TVPI7In4Qe+KwT9Tn12p/RevaLkol5FsNkYCmddZnlUDkafens0TfdN/Sx1y4XV0y5LkZ5r9Nh961KmDOnr+jkzjbt3n9Gg489OvIRV6MBpWywnF1B/2jSZpj/6vNZMu1MP9j5K0zqnxV5ybGehF8mrhpv1/OYZ588xFVSzCcCZec+HR38pvif36SY29m2m/Rt+6/Lx0H7T2aT43dAvac4tmDmatbb4x+NGtEaZf/rLJ8dihEq8x9+2UyDHVj+vy/oLzfG67TWW3t0+P2LwrU44iU6/zfqjW49EY07XokIabwuzqjf+7fx7bSyL/oJrHG5tukv73w+XYOzvnNAT8rWxInDnji0bSM7KzQ6zc122VmNotssWgHP/I773GJftCmSY20Cs7czN76ikzfm1mzOq/F2nROT57NX02E+EyhHvVfjfzqZfyBGpU2J+Wi27eroVv3/rfJPZoPjd/V6T3NsgbjK6/uxbNx/nSN7iRhQj9HMpFyl9YUvyomd+c/Gfklt3XlCp3YtxWjd0/WCtTi6hRl31hKeKdWFl7iyosQ+LNwwHNL56RPa3yhag6PF2n4BZW5bTS/HzVRYe5Piyt42cW9bTQOn2W2tVFjbujf/vDhrx9yQ7XFK7drEZAW4WZC/8QU9fMH9OMaWMQHmjkA5p+LZ2RH2ZJjb2bbxujafcbD58Tuk3u0Ykr3FbO3NjC0QV3YQauI9mU6YV/gwcZXnicg2cu7LKz+XlNVnUKGU6sJLXHF0JvUW+wcRk/UoW3c79CZ3qZ1tA2kNgCNBOvoV1Tbd6/yp4qL6hlg7VW8XhrPcU2rXTtyzHzNU5R6b+bxAoaURV/afndk/Wl7j4Fwd2Q+27zYzfo+jKKp3G19aYwvElW0/TbynNH28UP7A24ILfoyBa/y5icWNXoNKSnUhIa4WZhzFsc4c2l9kFv7yK8WpezvTV/QLx1kxF48mA35M1gtB2P/0mS++lNp1NnY7i1XpH4GYzBcFipe4SoH53GzbGLzXOJito9HnZsfvcUhF9Z7i2IIF7blNKZpx8iWa/YXSuBPEWERdVFJmoTETc5GnpRBXTLkaqYslElfDwXN6aLa62HlA3dGWDHxLyGfJtDPejdCZjzR48Yj2zfYA5kcEubNtZZcqGvDL8kqdL/niS6ldLxQ5hF9InoULexrsLUC7djT7ziw1SID5uK9l43U+M8s68sGUtLH8TMLW4npPa2wZFx0zV8JNoJq7op/sMv+JVrtAjdT2v4H5OMb35Ll1NTZPVhhO/rvO/vKwRnRVso47HjMQTh0lVBde4moSb5bpZDYgK9inxRQ7sLM+a17CanTZ0X/0mbYTNHtRtxB2LzFfYdU0a1Pesr7FLWpPoV2X8Mu9lVySJ/r2I7bNWcFVtI4nBeY23tl7+ThY1sZibK8TWO/JjC0z3hBXMxYNHNnGbBdtml2MO6Md0dk1FDGjnExvTxen+/w6ya69cRa0j9eFXA9Y0yJT2PJBxVwnobrwElf2loVtO6YMk005i349JoOUxptCmkXJ3Jd63oXswHmXHp+anbnsxqNV193k+fa1faQ3na9Gv67072PNsp6WbKFv2fFi/Guw/D35U2jXefxs3c/WBE3LOTrIyxOvfc/H4n7yEVcpMHdjHh97jYMLbcxubB1r/A6t9xTGlnnmEFfzPOJ/WnhMgtnF+IdkH3+T/al/XocdDnp04jyiw/wq6OhZn9m1Wx95Xoy5aydSqQtGXC2Ww2yU2nEeKWIeT/SQfppsQaFH1n7BOLcZJo9jmXv8Tk45Fh5REXubDhvTXLxOOSbrp9JhPV+L5X3L1o0zs5JEuy5vq6kyn6+BHL55i9yTYD4f+SJfsxx2cU+98jY271f+U3lbyY878ziu2GNLBgTEVQYIPoIACIAACIAACIBAHQIQV3XoIS8IgAAIgAAIgAAIZAhAXGWA4CMIgAAIgAAIgAAI1CEAcVWHHvKCAAiAAAiAAAiAQIYAxFUGCD6CAAiAAAiAAAiAQB0CEFd16CEvCIAACIAACIAACGQIQFxlgOAjCIAACIAACIAACNQhAHFVhx7yggAIgAAIgAAIgECGAMRVBgg+ggAIgAAIgAAIgEAdAhBXdeghLwiAAAiAAAiAAAhkCEBcZYDgIwiAAAiAAAiAAAjUIQBxVYce8oIACKwAgQ/UP75N63vH1B/mFWfyMFnuIdXDU3q89xs67L51MtuH927SjeNTynVLk+u2btPj/gcnLw5BAASWnQDE1bLXIOIHARCoScAKIUbkjMTTVdptv8h9+Piwf0w3Nu5T9ywjoUb5NnnRVna+ZqmQHQRAoDkCEFfNsceVQQAEEiEwEkit65nZJxPcRHhxs1b2fO6sV9HM1GQ2LPeaiUBBGCAAAsEEIK6C0SEjCIDAyhA469LhRs4tvJJZK6K31D34DX/rb+J3cdbL5LtO63kzXisDFQUBgctLAOLq8tY9Sg4CIGAJTG7RbR106cza6CO96XxFW0UCaCSemNuJIz+MiOLE3PTaOAABEFhmAhBXy1x7iB0EQECIwEQEubf3zl/Q0c5VflbK3DTk1ls5US3ecixZ4+XkxSEIgMByEoC4Ws56Q9QgAAKiBCbro6azVJNZq52H1DvPLFSfXnecZ362a3pydrAwKzYWclt3O/SGcz3LjSMQAIElJABxtYSVhpBBAASkCWRmk0azVtfpXudPzDYKZtoqbwuGvLjsovjxLwqHbzp0byNv8XxeXthAAASWkQDE1TLWGmIGARAQJzC7ffdqvO9V4awVEZWut3JCHKU1gsrTt5MVhyAAAstHAOJq+eoMEYMACGgQsIvMf/839J9KZ5Yms1HuGq3CmCa3EP/j39Df7BWv4yp0g5MgAAJLQQDiaimqCUGCAAioE5hsu/Dvd35DW6WiyaybKtiCISfY8czYGq2ze2blZIIJBEBgKQlAXC1ltSFoEAABeQKTXwy2btJR732xe+/1Vq6byUL2ue0e3PM4BgEQWBUCEFerUpMoBwiAAAiAAAiAQBIEIK6SqAYEAQIgAAIgAAIgsCoEIK5WpSZRDhAAARAAARAAgSQIQFwlUQ0IAgRAAARAAARAYFUIQFytSk2iHCAAAiAAAiAAAkkQgLhKohoQBAiAAAiAAAiAwKoQgLhalZpEOUAABEAABEAABJIgAHGVRDUgCBAAARAAARAAgVUhAHG1KjWJcoAACIAACIAACCRBAOIqiWpAECAAAiAAAiAAAqtCAOJqVWoS5QABEAABEAABEEiCwP8PhD0Hk48G/9gAAAAASUVORK5CYII=" width="532" height="357"></p>
</div>
<div class="specification">
<p>Component X and a cell of negligible internal resistance are placed in a circuit.</p>
<p>A variable resistor R is connected in series with component X. The ammeter reads <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi>mA</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" width="187" height="157"></p>
</div>
<div class="specification">
<p>Component X and the cell are now placed in a potential divider circuit.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARIAAACVCAYAAACU9XX3AAARE0lEQVR4Ae2dwWsbSRbG5z+RQScZBDPk4lNmd9mD44MJOYSBXHbJBOKBgdwW4uC9zGFnAzbkMDnN2qznsAwMMjO3zYDYSw4GQQ57MDoshInRIYRgDAnGiLc8SdVSd1d3Vatfl6q6P4Gw1FX96r1fvf5UVd3u/oTwAgEQAIGSBD4puT92BwEQAAGCkCAJQAAEShOAkJRGCAMgAAIQEuQACIBAaQIQktIIYQAEQABCghwAARAoTSA4IWm31gjv+jAoncEw4AWBIIXEC3JwojQB/kHAqx4EICT16Mcgo4CQBNltWqchJFos2OiCAITEBWU3bUBI3HBGKxoCEBINlEA3QUgC7bg6uA0hqUMvTmOAkNSnL4OLBEISXJdlOgwhyUSDgqoJQEiqJuzOPoTEHWu0lCAAIUkACfgrhCTgzgvddQhJ6D049x9CMmeBT44JQEgcA6+wOQhJhXBhOp8AhCSfT0ilEJKQeqtmvkJI6tOhEJL69GVwkUBIguuyTIchJJloUFA1AQhJ1YTd2YeQuGONlhIEICQJIAF/hZAE3Hmhuw4hCb0H5/5DSOYs8MkxAQiJY+AVNgchqRBu002zUEi8m84xhPjtheTylA4216l9v0ejnMjGo1M63t2eJ1DnSzroDWg0XtxpTBf9Peq21un24RnFiqJqH2l4eI/arXt0NPwYbcWvWITC+w8SfSVhw3tQNXDQUkje02D/zlQccoXkLfV3b1J7c49OhhdEdEWj/je0pROM8Rkdba9Te/uQhjolyShHYoWTdRJ9JWEjHGLhemohJGO6HDyjLTVMzROSiz496SRGGUoQUvvpRxxTlKrNm/Sk/zZGF4kVw+H1F4m+krDhNaSaOGcWksmU5jPa+ttTevLpWu7U5nqwTzdayYP/kgb7t6jd2aP+RWLoMROerf1TuowBnY1sNPsgsWKgvP6S6qtRjx6oH6TE3+79fToZjFLT3JQNryNurnMGIZlNaTaf0eD9KR3kCola97hFB4NFWVAjj6/pZHSdIJ0hGLqRzWxPJFYCocdfU301EZLP6EHvt7jX43Pq7/G6Wnw9jCulbMT3xDdPCOQIiZpe3KGDwXui64FBSK5p1Pua2q2kkKjtOiEhGg8P6XZsFKMEKZ1USCxPssbSjZQIZAkJ25v8eKzRjf0BLf7cpGxYto1qbglkC4ma0qhpR0VCQrM1lO5un3h5lmg6Suk+7NF5YibEpUgstwlSprVUX+UJySy/5nkwbTllo4xD2LcyAhlCsjCluZwdzUYhUSOJ5Igkb2rDcc32m62HjM97tNNJrrPM40dizVn4/inVVzlCMh2ZJhbq8cPhexdH/umFRIlGYkGME2P61k9TCi+2Kjcmw1oWj9+m147wmowSMFVn9jeVnIlyfPWHQKqvMoQkuvao84hOzq9iAaRsxErxxRcCeiHReafEJXUad6GybpFUnf7Nul5ksvt01NL9y1N6uv1ZzkVqmNos0Pb+Y0oEJkKifowW/67T1u4h9SfXHsXDStmIF+ObJwRkhWS2vtHuPKSjM17xuKBhb4+2Whu003udOrW3yGA6tF2jtuZXabEeEmuRht+fU32VMSLJiyJlI68yylZGoJyQaEYp0TA1mgZt05N/niYukdfFO1tkjRZddXUwItFT8XNrSgQgJH52lIBX9kIi0JiEiVRyShiFjUoIpPoKQlIJZx+MQkh86IWa+gAhqWnHasKCkGigYJMMAQiJDMcQrEBIQuilQH1MCckScUjYWKJZ7FKQAISkIDBUtycgIQISNuw9Rs1lCUBIliWH/YwEJERAwobRUVQoTQBCUhohDGQRkBABCRtZ/mG7HIHKhYQTwee3HEpYShKQEAEJG0m/8F2eQOVCIu8yLIZCQEIEJGyEwitkPyEkIfee575LiICEDc8x1cI9CEktutHPICREQMKGn3Tq5RWEpF796VU0EiKQaWM8okFvnx50FtbgtI8+8QpJbZ2BkNS2a1cfWKYIFHBNa2P8mk4ebiw89oQNXtHo9PlEWLLurlegWVQtSABCUhAYqtsT0IqA/e6Tmjob01tOaG4iTepufPr7/RZsGtULEICQFICFqsUI6ESgmAX9bSOmd+JL35axqG3UlyMAIZFjCUsJAlUJCanHx7Y26MH+v+gXzfNwEq7ga8UEICQVA26y+cqEhMZ0Ofw3HdzfWLjYkW/X+D2d/Jx8znSTe8Bd7N4ICSed9NsdRrSkI1CdkMxbG48G9EvvJzpaeHB99/4xnWXcPHy+Jz5JEvBGSGyDkkhO27ZQrxwBib4qZOPyjE4mgpL9OJNyEWHvLAIQkiwy2F6aQCERyGitqA11E/HkE/syzGOzEAEIiRBImEkTKCoCaQu6szYZz4tWO0/uC4sRicLh6i+ExBXpBrZTjZAQTZ/GuEbd+/t0snDGRj3BAGsk7pMNQuKeeWNarEpIGOBkkfVwl7YWF+n5Evmf/kNDLLQ6zzEIiXPkzWmwSiFpDsUwIoWQhNFPQXpZpZC8efOGXrx4ESSXOjoNIaljr3oSk6SQvHv3jl6+fEnPv3tOX9y9G11z5EmojXcDQtL4FKgOgJSQfLWzEwkH28R7rbpOW9IyhGRJcNjNTEBKSIbDIZ30erT7+HFKRMxe1K+GBFdpKhASaaKwFxGQSPikjQ8fPtCrV6/oh+Nj4pFKE19JJj4wgJD40As19UEi4SVs1A2vj0wgJHXLMo/ikUh4CRseIRFxxUcmEBKRroURHQGJhJewofMt5G0+MoGQhJxRnvsukfASNjzHVNg9H5lASAp3I3awJSCR8BI2bP0NpZ6PTCAkoWRPgH5KJLyEjQDR5brsIxMISW6XobAMAYmEl7BRJgYf9/WRCYTEx0ypiU8SCS9hoyY4ozB8ZAIhiboHH6QJSCS8hA3puFZtz0cmEJJVZ0WN25dIeAkboSNmBqb3qmOEkKy6B2rcvoQISNgIHbGJgancRfwQEheUG9qGRIJL2Agdv4mBqdxF/BASF5Qb2oZEgkvYCB2/iYGp3EX8EBIXlBvahkSCS9gIHb+JgancRfwQEheUG9qGRIJL2Agdv4mBqdxF/BASF5Qb2oZEgkvYCB2/iYGp3EX8EBIXlBvahkSCS9gIHb+JgancRfwQEheUG9qGRIJL2Agdv4mBqdxF/BASF5Qb2oZEgkvYCB2/iYGp3EX8EBIXlBvahkSCS9gIHb+JQXb5FZ33HlG3tUE7vdc0joEY0+XZMT3orNPW3q80ihfGatp8gZDYUEKdpQikE/yChv0f6eD+xvySb8NjNtM2lnIl6J1MDHLLx6/p5OEGtTuP6OT8as7h8pQONtepvfmMBgKPOIWQzNHikzCBWIKPz6m/t01tFo5fh3Q5aeuKRoPeVFg2v6H+aCHRZ77EbAj7F4o5EwNTefTQ9Yc9Op+MPN7TYP8OtVt36GDwXgQDhEQEI4zoCMwTXA2xMxJ39uvYjRJ9bm1uY76taZ9MDEzlRIo/T3H+RxeDZ7TVWqet/dOZoJcnCiEpzxAWMghECX7RpyedNeru9ulCW3dMF/096rbu0dHwY6xGZCO2tVlfTAxM5RNaaoqj/pNYaEqjegJCokjgrzgBleDXg3260bpJT/pvs9sY9ehBa51uH57FFgWVjewd619iYmAqV4TUFKetEWxVZ9m/EJJlyWE/I4FpgqvRxi06GExXRrQ7Xg/o4NM1urE/oOuFCrYHycIutftoYmAqnwJR0xu+t4nstIbtQ0hql3b+BAQhkekLk1CYyonUqd416t7/hp5OzpplrFct6TKEZElw2M1MQCW4/dQGIxIdVcVRV8bbTOWkTvXOTgFHUxzBdRIISVbvYHtpAlGCWy+2ptdRIhulvQnXgIlBfrk61btNf+2fz9af1DRHbooDIQk3v7z3fJ7gKnEXh9Nvqb97k9qbu3Tc/4me8sVRnT3qX8QvsZzb8D7cyhw0McguH9Nl1qne6CzOYp8sHwKEZHl22NNAIJbgugvSLv9LR9FVrou/mHPDMRvzzY36ZGKQVW6awpjKi0CGkBShhbqFCKQTXHOJfGuNun/6kv7cWZte9dobxP7vI22jkAu1qGxiYCp3AQFC4oJyQ9solODjEQ1+7tEvgxGuI0nki4mjqTxhrpKvEJJKsMIoE5BIcAkbofeGiYGp3EX8EBIXlBvahkSCS9gIHb+JgancRfwQEheUG9qGRIJL2Agdv4mBqdxF/BASF5Qb2gYnuMS7ofiisE1CYSqPDFX4AUJSIVyYzifgwwGQ76EfpSZOpnIXUUBIXFBGG1oCPhwAWsc822jiZCp3EQ6ExAVltKEl4MMBoHXMs40mTqZyF+FASFxQRhtaAj4cAFrHPNto4mQqdxEOhMQFZbShJeDDAaB1zLONJk6mchfhQEhcUEYbWgI+HABaxzzbaOJkKncRDoTEBWW0oSXgwwGgHHvz5g2d9Hq0+/gxfXH3bnTamr8//+45vXz5kj58+KCqO/1r4mQqd+EshMQFZbShJeDDAcACwcLB7x+Oj+nVq1fEosIvFo7hcEgvXrygv3/77URcWFRcC4qJk6lcC194I4REGCjM2RNY5QHAYqBGHywmNq93795NRie///zzyQjFZh+JOszJ9JZop4wNCEkZeti3FIFVCQmPOHgEsuzogkcpLCY8glnFa1Xc8mKFkOTRQVmlBFZxQPBIhEWARaTMi8WI7fC0x/VrFdxMMUJITIRQXhmBVRwQavFUIiglJjxCcflaBTdTfBASEyGUV0bA9QGhFlZNi6Xj4SHd5nUJzT1kkzB4RMLTJJcv19xsYoOQ2FBCnUoIuD4g+IA3L6zO7rr+x1u01Uk/+U8Hws6ubs/ltrnmZuMlhMSGEupUQsDlAcGnda1GDpNHZ6zT7e9/pH9sr1N7+5CG8Rvbp1iwOH21s5PaXtUGl9xsY4CQ2JJCPXECLg8IXlzlC87yX+rxovx8nd9oeHiPbJ6Ty1MljoVPD7t4ueRmGw+ExJYU6okTcHlA8IjBvCg6e9bObG1kulZiN73hRVwe9bh4ueRmGw+ExJYU6okTcHlAWLWVfCLg+IyOLKc3fE2JecQjg9AqFpmmrK1ASKxRoaI0AZcHhLkt9TTAe3Q0/DgL9eNsepN+lGiSBYsIhCRJxePvnBB4g8EyOZCb1mr0kZFf3d0+XeQYYBH5w+9+7yw3c1xZSVFwI5KVUEKjwRNg4clbDM1eD4mvm2SB4MXcVVzlmuWP6+0QEtfE0d5KCOQvhs6mMJ1HdHJ+lfBv8UzO20TZ/KvdYu68ft0+QUjq1qOIR0uAF0Mz/79mNq3JnL6oRdiHPTrXXFPCIx0e8TT5BSFpcu83KHb1fzHpy+PHdDl4RlutvAXV2dWurcWF2Dk8Xh/h+5U0+QUhaXLvNyx2nt5In1lR/01svkal3rAhJPXuX0S3QEDdR4RHJ1Ivni6xQDX9BSFpegY0LH5eK+GF0fQUpzgI/h8bvieJhK3irfu1B4TEr/6ANw4I8CiirJgoEZEc3TgIvbImICSVoYVhnwmwmPB/Axdd2+DRB49qeCQCEZn3MIRkzgKfGkaALyBTt100iQILiLqJEa+J5F3c1jCMk3AhJE3sdcQcEWCB4DM5LCg8QuGRCn9ffLNw8HUi/LfoCCZqqOYfICQ172CEZ0+ARYJHHYsiwp/59gAYgeRzhJDk80EpCICABQEIiQUkVAEBEMgnACHJ54NSEAABCwIQEgtIqAICIJBPAEKSzwelIAACFgQgJBaQUAUEQCCfAIQknw9KQQAELAhASCwgoQoIgEA+AQhJPh+UggAIWBCAkFhAQhUQAIF8AhCSfD4oBQEQsCAAIbGAhCogAAL5BCAk+XxQCgIgYEHg/yds68zIN+roAAAAAElFTkSuQmCC" width="241" height="131"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why component X is considered non-ohmic.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the resistance of the variable resistor.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power dissipated in the circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Slider S of the potential divider is positioned so that the ammeter reads <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>mA</mtext></math>. Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">current is not «directly» proportional to the potential difference<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">resistance of X is not constant<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">resistance of X changes «with current/voltage» </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="fontstyle0">voltage across X<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">voltage across R<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">resistance of variable resistor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>overall resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>200</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<p>resistance of X <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>115</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<p>resistance of variable resistor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>200</mn><mo>-</mo><mn>115</mn><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>020</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>080</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">W</mi><mo>»</mo></math> <span class="fontstyle0">✓</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mi>mA</mi></math> </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>current from the cell is greater «than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>mA</mtext></math>» ✓</p>
<p>because some of the current must flow through section SQ of the potentiometer ✓</p>
<p>overall power greater «than in part (b)» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>total/overall resistance decreases ✓</p>
<p>because SQ and X are in parallel ✓</p>
<p>overall power greater «than in part (b)» ✓</p>
<p><br><em>Allow the reverse argument.</em></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most answers that didn't score simply referred to the shape of the graph without any explanation as to what this meant to the relationship between the variables.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question produced a mixture of answers from the 2 alternatives given in the markscheme. As a minimum, many candidates were able to score a mark for the overall resistance of the circuit.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A straightforward calculation question that most candidates answered correctly.</p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Surprisingly a significant number of candidates had difficulty with this. Answers of 20 mA and 4 V were often seen.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. This question challenged candidate's ability to describe clearly the changes in an electrical circuit. It revealed many misconceptions about the nature of electrical current and potential difference, of those who did have a grasp of what was going on the explanations often missed the second point in each of the markscheme alternatives as detail was missed about where the current was flowing or what was in parallel with what.</p>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Satellite Y orbits closer to the centre of Earth than satellite X. Outline why</p>
</div>
<div class="specification">
<p>The cable acts as a spring. Satellite Y has a mass <em>m</em> of 3.5 x 10<sup>2</sup> kg. Under certain circumstances, satellite Y will perform simple harmonic motion (SHM) with a period <em>T</em> of 5.2 s.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X orbits 6600 km from the centre of the Earth.</p>
<p>Mass of the Earth = 6.0 x 10<sup>24</sup> kg</p>
<p>Show that the orbital speed of satellite X is about 8 km s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the orbital times for X and Y are different.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>satellite Y requires a propulsion system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cable between the satellites cuts the magnetic field lines of the Earth at right angles.</p>
<p><img 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"></p>
<p>Explain why satellite X becomes positively charged.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The magnetic field strength of the Earth is 31 μT at the orbital radius of the satellites. The cable is 15 km in length. Calculate the emf induced in the cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the value of <em>k</em> in the following expression.</p>
<p><em>T</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2\pi \sqrt {\frac{m}{k}} ">
<mn>2</mn>
<mi>π</mi>
<msqrt>
<mfrac>
<mi>m</mi>
<mi>k</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{G{M_E}}}{r}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mrow>
<msub>
<mi>M</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.0 \times {{10}^{24}}}}{{6600 \times {{10}^3}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6600</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>7800 «m s<sup>–1</sup>»</p>
<p><em>Full substitution required</em></p>
<p><em>Must see 2+ significant figures.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Y has smaller orbit/orbital speed is greater so time period is less</p>
<p><em>Allow answer from appropriate equation</em></p>
<p><em>Allow converse argument for X</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to stop Y from getting ahead</p>
<p>to remain stationary with respect to X</p>
<p>otherwise will add tension to cable/damage satellite/pull X out of its orbit</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>cable is a conductor and contains electrons</p>
<p>electrons/charges experience a force when moving in a magnetic field</p>
<p>use of a suitable hand rule to show that satellite Y becomes negative «so X becomes positive»</p>
<p><em><strong>Alternative 2</strong></em></p>
<p>cable is a conductor</p>
<p>so current will flow by induction flow when it moves through a B field</p>
<p>use of a suitable hand rule to show current to right so «X becomes positive»</p>
<p><em>Marks should be awarded from either one alternative or the other.</em></p>
<p><em>Do not allow discussion of positive charges moving towards X</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electrons would build up at satellite Y/positive charge at X</p>
<p>preventing further charge flow</p>
<p>by electrostatic repulsion</p>
<p>unless a complete circuit exists</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>ε</em> = <em>Blv =</em>» 31 x 10<sup>–6</sup> x 7990 x 15000</p>
<p>3600 «V»</p>
<p><em>Allow 3700 «V» from v = 8000 m s<sup>–1</sup>.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>k</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4{\pi ^2}m}}{{{T^2}}} = ">
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4 \times {\pi ^2} \times 350}}{{{{5.2}^2}}}">
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>350</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>5.2</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>510</p>
<p>N m<sup>–1</sup> <em><strong>or</strong> </em>kg s<sup>–2</sup></p>
<p><em>Allow MP1 and MP2 for a bald correct answer</em></p>
<p><em>Allow 500</em></p>
<p><em>Allow N/m etc.</em></p>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>p</sub> in the cable/system transfers to <em>E</em><sub>k</sub> of Y</p>
<p>and back again twice in each cycle</p>
<p><em>Exclusive use of gravitational potential energy negates MP1</em></p>
<div class="question_part_label">f.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The primary coil of a transformer is connected to a 110 V alternating current (ac) supply. The secondary coil of the transformer is connected to a 15 V garden lighting system that consists of 8 lamps connected in parallel. Each lamp is rated at 35 W when working at its normal brightness. Root mean square (rms) values are used throughout this question.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the total resistance of the lamps when they are working normally.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the current in the primary of the transformer assuming that it is ideal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A pendulum with a metal bob comes to rest after 200 swings. The same pendulum, released from the same position, now swings at 90° to the direction of a strong magnetic field and comes to rest after 20 swings.</p>
<p style="text-align:center;"> <img src="data:image/png;base64,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"></p>
<p>Explain why the pendulum comes to rest after a smaller number of swings.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mn>15</mn><mn>110</mn></mfrac><mo>×</mo><mn>3300</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>450</mn><mo> </mo><mo>«</mo><mtext>turns</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>calculates total current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">=</mi><mfrac><mn>35</mn><mn>15</mn></mfrac><mo>×</mo><mn>8</mn><mo>«</mo><mo>=</mo><mn>18</mn><mo>.</mo><mn>7</mn><mtext> A</mtext><mo>»</mo></math>✓</p>
<p>resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mfrac><mn>15</mn><mrow><mn>18</mn><mo>.</mo><mn>7</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math> ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>calculates total power <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>= 35</mo><mo>×</mo><mn>8</mn><mo> </mo><mtext>« = 280 W»</mtext></math> ✓</p>
<p>resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mfrac><msup><mn>15</mn><mn>2</mn></msup><mn>280</mn></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math>✓</p>
<p><em><strong><br>ALTERNATIVE 3</strong></em></p>
<p>calculates individual resistance<em> </em><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><msup><mn>15</mn><mn>2</mn></msup><mn>35</mn></mfrac><mo>«</mo><mo>=</mo><mn>6</mn><mo>.</mo><mn>43</mn><mo> </mo><mtext>Ω</mtext><mo>»</mo></math>✓</p>
<p>resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>43</mn></mrow><mn>8</mn></mfrac><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math>✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total power required = 280 «W»<em><strong><br>OR<br></strong></em>uses factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3300</mn><mn>450</mn></mfrac></math><em><strong><br>OR<br></strong></em>total current = 18.7 « A» <strong>✓</strong><em><strong><br></strong></em></p>
<p>current = 2.5 <em><strong>OR</strong> </em>2.6 «A» <strong>✓</strong></p>
<p><em><br>Award <strong>[2] marks</strong> for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from (a)(ii).</em></p>
<p> </p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the secondary coil does not enclose all flux «lines from core» <strong>✓</strong></p>
<p>induced emf in secondary<br><em><strong>OR</strong></em><br>power transferred to the secondary<br><em><strong>OR</strong></em><br>efficiency is less than expected <strong>✓</strong></p>
<p><em><br>Award <strong>[0]</strong> for references to eddy currents/heating of the core as the reason.</em></p>
<p><em>Award <strong>MP2</strong> if no reason stated.</em></p>
<p> </p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>bob cuts mag field lines<br><em><strong>OR</strong></em><br>there is a change in flux linkage <strong>✓</strong></p>
<p>induced emf across bob <strong>✓</strong></p>
<p>leading to eddy/induced current in bob <strong>✓</strong></p>
<p>eddy/induced current produces a magnetic field that opposes «direction of» motion <strong>✓</strong></p>
<p>force due to the induced magnetic field decelerates bob <strong>✓</strong></p>
<p>damping of pendulum increases/there is additional «magnetic» damping <strong>✓</strong></p>
<p><em><strong><br>MP4</strong> and <strong>MP5</strong> can be expressed in terms of energy transfer from kinetic energy of bob to electrical/thermal energy in bob</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Rhodium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,45}^{106}{\text{Rh}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>45</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Rh</mtext>
</mrow>
</math></span>) decays into palladium-106 (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="_{\,\,\,46}^{106}{\text{Pd}}">
<msubsup>
<mi></mi>
<mrow>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mn>46</mn>
</mrow>
<mrow>
<mn>106</mn>
</mrow>
</msubsup>
<mrow>
<mtext>Pd</mtext>
</mrow>
</math></span>) by beta minus (<em>β</em><sup>–</sup>) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the <em>β</em><sup>–</sup> decay.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.42.36.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/09.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Bohr modified the Rutherford model by introducing the condition <em>mvr </em>= <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span>. Outline the reason for this modification.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed <em>v </em>of an electron in the hydrogen atom is related to the radius <em>r </em>of the orbit by the expression</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>k </em>is the Coulomb constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the answer in (b) and (c)(i), deduce that the radius <em>r </em>of the electron’s orbit in the ground state of hydrogen is given by the following expression.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}">
<mi>r</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>k</mi>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electron’s orbital radius in (c)(ii).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what may be deduced about the energy of the electron in the <em>β</em><sup>–</sup> decay.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest why the <em>β</em><sup>–</sup> decay is followed by the emission of a gamma ray photon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the gamma ray photon in (d)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the electrons accelerate and so radiate energy</p>
<p>they would therefore spiral into the nucleus/atoms would be unstable</p>
<p>electrons have discrete/only certain energy levels</p>
<p>the only orbits where electrons do not radiate are those that satisfy the Bohr condition <strong>«</strong><em>mvr</em> = <em>n</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{m_{\text{e}}}{v^2}}}{r} = \frac{{k{e^2}}}{{{r^2}}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><strong><em>OR</em></strong></p>
<p>KE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>PE hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>m</em><sub>e</sub><em>v</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\frac{{k{e^2}}}{r}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><strong>«</strong>solving for <em>v </em>to get answer<strong>»</strong></p>
<p> </p>
<p><em>Answer given – look for correct working</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>combining <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} ">
<msqrt>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
</msqrt>
</math></span> with <em>m</em><sub>e</sub><em>vr</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{h}{{2\pi }}">
<mfrac>
<mi>h</mi>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span> using correct substitution</p>
<p><strong>«</strong><em>eg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}">
<msup>
<mrow>
<msub>
<mi>m</mi>
<mi>e</mi>
</msub>
</mrow>
<mn>2</mn>
</msup>
<mfrac>
<mrow>
<mi>k</mi>
<mrow>
<msup>
<mi>e</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mtext>e</mtext>
</mrow>
</msub>
</mrow>
<mi>r</mi>
</mrow>
</mfrac>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>h</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p>correct algebraic manipulation to gain the answer</p>
<p> </p>
<p><em>Answer given – look for correct working</em></p>
<p><em>Do not allow a bald statement of the answer for MP2. Some further working eg cancellation of m or r must be shown</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong> <em>r</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{4{\pi ^2} \times 8.99 \times {{10}^9} \times 9.11 \times {{10}^{ - 31}} \times {{(1.6 \times {{10}^{ - 19}})}^2}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>8.99</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>9</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>9.11</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p><em>r</em> = 5.3 × 10<sup>–11</sup> <strong>«</strong>m<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the energy released is 3.54 – 0.48 = 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p>this is shared by the electron and the antineutrino</p>
<p>so the electron’s energy varies from 0 to 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the palladium nucleus emits the photon when it decays into the ground state <strong>«</strong>from the excited state<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Photon energy</p>
<p><em>E</em> = 0.48 × 10<sup>6</sup> × 1.6 × 10<sup>–19</sup> = <strong>«</strong>7.68 × 10<sup>–14</sup> <em>J</em><strong>»</strong></p>
<p><em>λ</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{hc}}{E} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{7.68 \times {{10}^{ - 14}}}}">
<mfrac>
<mrow>
<mi>h</mi>
<mi>c</mi>
</mrow>
<mi>E</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.63</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>34</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>7.68</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>14</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 2.6 × 10<sup>–12</sup><strong> «</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from incorrect energy</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.57.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/04"></p>
<p>The following data are available for the conductor:</p>
<p> density of free electrons = 8.5 × 10<sup>22</sup> cm<sup>−3</sup></p>
<p> resistivity ρ = 1.7 × 10<sup>−8</sup> Ωm</p>
<p> dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.</p>
<p> </p>
<p>The ammeter reading is 2.0 A.</p>
</div>
<div class="specification">
<p>The electric field <em>E </em>inside the sample can be approximated as the uniform electric field between two parallel plates.</p>
</div>
<div class="specification">
<p>An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.57.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/04"></p>
<p>The following data are available for the conductor:</p>
<p> density of free electrons = 8.5 × 10<sup>22</sup> cm<sup>−3</sup></p>
<p> resistivity ρ = 1.7 × 10<sup>−8</sup> Ωm</p>
<p> dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.</p>
<p> </p>
<p>The ammeter reading is 2.0 A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the resistance of the conductor.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the drift speed <em>v </em>of the electrons in the conductor in cm s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the electric field strength <em>E</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{E} = \frac{1}{{ne\rho }}">
<mfrac>
<mi>v</mi>
<mi>E</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>ρ</mi>
</mrow>
</mfrac>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1.7 × 10<sup>–8</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.10}}{{{{(0.02 \times {{10}^{ - 2}})}^2}}}">
<mfrac>
<mrow>
<mn>0.10</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.02</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>0.043 <strong>«</strong>Ω<strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>v</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{I}{{neA}}">
<mfrac>
<mi>I</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>A</mi>
</mrow>
</mfrac>
</math></span><strong>»</strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{{8.5 \times {{10}^{22}} \times 1.60 \times {{10}^{ - 19}} \times {{0.02}^2}}}">
<mfrac>
<mn>2</mn>
<mrow>
<mn>8.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>22</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>0.02</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>0.37 <strong>«</strong>cms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em> = <em>RI</em> = 0.086 <strong>«</strong><em>V</em><strong>»</strong></p>
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{V}{d} = \frac{{0.086}}{{0.10}} = ">
<mfrac>
<mi>V</mi>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.086</mn>
</mrow>
<mrow>
<mn>0.10</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span><strong>»</strong> 0.86 <strong>«</strong>V m<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from 4(a).</em></p>
<p><em>Allow ECF from MP1.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>clear use of Ohm’s Law (<em>V </em>= <em>IR</em>)</p>
<p>clear use of <em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\rho L}}{A}">
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>L</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></p>
<p>combining with <em>I </em>= <em>nAve </em>and <em>V </em>= <em>EL </em>to reach result.</p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>attempts to substitute values into equation.</p>
<p>correctly calculates LHS as 4.3 × 10<sup>9</sup>.</p>
<p>correctly calculates RHS as 4.3 × 10<sup>9</sup>.</p>
<p> </p>
<p><strong><em>For ALTERNATIVE 1 look for:</em></strong></p>
<p><em>V</em> = <em>IR</em></p>
<p><em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\rho L}}{A}">
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>L</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></p>
<p><em>V</em> = <em>EL</em></p>
<p><em>I</em> = <em>nAve</em></p>
<p><em>V</em> = <em>I</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\rho L}}{A}">
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>L</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></p>
<p><em>EL</em> = <em>I</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\rho L}}{A}">
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>L</mi>
</mrow>
<mi>A</mi>
</mfrac>
</math></span></p>
<p><em>E</em> = <em>I</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\rho }{A}">
<mfrac>
<mi>ρ</mi>
<mi>A</mi>
</mfrac>
</math></span></p>
<p><em>E</em> = <em>nAve</em><em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\rho }{A}">
<mfrac>
<mi>ρ</mi>
<mi>A</mi>
</mfrac>
</math></span> = nveρ</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{E} = \frac{1}{{ne\rho }}">
<mfrac>
<mi>v</mi>
<mi>E</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>ρ</mi>
</mrow>
</mfrac>
</math></span></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a potential divider circuit used to measure the emf <em>E </em>of a cell X. Both cells have negligible internal resistance.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_13.01.10.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/04"></p>
</div>
<div class="specification">
<p>AB is a wire of uniform cross-section and length 1.0 m. The resistance of wire AB is 80 Ω. When the length of AC is 0.35 m the current in cell X is zero.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the emf of a cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the resistance of the wire AC is 28 Ω.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine <em>E</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Cell X is replaced by a second cell of identical emf <em>E </em>but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the work done per unit charge</p>
<p>in moving charge from one terminal of a cell to the other / all the way round the circuit</p>
<p> </p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for “energy per unit charge provided by the cell”/“power per unit current”</em></p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for “potential difference across the terminals of the cell when no current is flowing” </em></p>
<p><em>Do not accept “potential difference across terminals of cell”</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the resistance is proportional to length / see 0.35 <strong><em>AND </em></strong>1«.00»</p>
<p>so it equals 0.35 × 80</p>
<p><strong>«</strong>= 28 Ω<strong>»</strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current leaving 12 V cell is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{80}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
</math></span> = 0.15 <strong>«</strong>A<strong>»</strong></p>
<p><strong><em>OR</em></strong></p>
<p><em>E</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{80}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
</math></span> × 28</p>
<p><em>E</em> = <strong>«</strong>0.15 × 28 =<strong>»</strong> 4.2 <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow a 1sf answer of 4 if it comes from a calculation.</em></p>
<p><em>Do not allow a bald answer of 4 </em><strong>«</strong><em>V</em><strong>»</strong></p>
<p><em>Allow ECF from incorrect current</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>since the current in the cell is still zero there is no potential drop across the internal resistance</p>
<p>and so the length would be the same</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two equal positive fixed point charges <em>Q</em> = +44 μC and point P are at the vertices of an equilateral triangle of side 0.48 m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAEiCAYAAACx7u2JAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAArbSURBVHhe7dsPbJT1Hcfx77qEDUqapSygtOVvbjQ4hzAxrBj5Y4IEhDTrwtycW0UDROECaKJtcZljCiQKCiIJSiBYiVkmVpgJEwSRyYjYZgxnJhcpNi1/MulGKUPIuNs95QcDy12vn/bufoT3K2n4PQ8XNOV53+/h+V6/EYszAJ2S434F0AmEAwgIBxAQDiAgHEBAOICAcAAB4QACwgEEhAMICAcQEA4g4EOeHjl79qx9+OGfbefOXe6M2fDhw23KlCmWn5/vznzN8Rp7+I659q47vFLupIW25JGf2/RRN/EO2c0IxxMHDhywcHie1dcfdmeutnLlS1ZaWuqOrtAWzq/jL3jHXi0tcifjokft/d/Mtl9uyLPfvrfOykPfdr+B7sAbkQeampps2rSpCaMJhMNzbceO7e4oBTn9bfzjj9kDubvthT9+av91p9E9CMcDCxYscKvkZs580Jqbm91RCnrl2Xe/ZXbuyxb7jzuF7kE4WRbsNvv27XVHHaurq3WrjkXr/2a7mnMtFLrZertz6B6Ek2X79+93q9TU1ta5VXLR4/vt9Q1v2l9zJ9vMSYP5i+5mfD+vM6dOnXKrKzXbu+Ef2YABhZe/Bt3xC3vdymzjlsVW2r+Hex26C+FkWd++fd0qNUVFVzw5uyzfJq38izU0NF7x9Zlte6bcxofy3GvQnQgny4qLi90qNSUlJW6FbCKcLAsGm88+u9QdJTd16jQbMWKEO0I2EY4HysrK2qJIZvDgIbZo0SJ3hGwjHA/07NnT1qxZ0/bpgCCQr6uoqLJt2/5kBQUF7gyyjY/ceCb4vFpjY6M7MissLGwLC34hHEDArZqnglkM/EU4gIBwAAHhAALCAQSEAwh4HA0I2HEAAeEAAsLxFANQvxEOICAcQEA4gIBwAAFzHEDAjgMICAcQEA4gIBxPMQD1G+EAAsIBBIQDCAgHEDAABQTsOICAcAAB4XiKOY7fCAcQEA4gIBxAQDiAgHAAAQNQQMCOAwgIBxAQjqcYgPqNcAAB4QACwgEEhAMImOMAAnYcQEA4gIBwAAHheIoBqN8IBxAQDiAgHEBAOICAASggYMcBBIQDCAjHU8xx/EY4gIBwAAHhAALCAQSEAwgYgAICdhxAQDiAgHA8xQDUb4QDCAgHEBAOICAcQMAcBxCw4wACwgEEhAMICMdTDED9RjiAgHAAAeEAAsIBBAxAAQE7DiAgHEBAOJ5ijuM3wgEEhAMICAcQEA4gIBxAwAAUELDjAALCAQSE4ykGoH4jHEBAOICAcAAB4QAC5jiAgB0HEBAOICAcQEA4nmIA6jfCAQSEAwgIBxAQDiBgAAoI2HEAAeEAAsLxFHMcvxEOICAcQEA4gIBwAAHhAAIGoICAHQcQEA4gIBxPMQD1W0bCaW5uturqapsxY0bbBRF8VVZW2t69e90rgNRFIhFbtmyZjRt3V9u1FPy6Zs2atvOZkvaHAwcOHLBweJ7V1x92Z642deo0W758ufXs2dOdQSC4IBoaGt0RLgkCWbLkGXfU3sqVL1lpaak7Sp+07jhNTU1Jowm8885WW7x4sTsCEgvuWpJFEwiH52bkTiat4axevTppNJdUV2/ktg1JBbf7lZVPuqPkKiqetLNnz7qj9EhbOMH/eBBEqvbs2eNWCHCbdrW6ulq36ljwZn3o0CF3lB5pC6exsXN/8bW1qX9jcOOpra1zq9TU19e7VXpk5KlaKk6cOO5WgP/SFk6fPn3cKjVjx97pVggwx7nasGHD3Co1ffv2dav0SFs4+fn5bY+aUzVx4gS3AtobPXq0W6Vm5MiRbpUeab1VW7hwoVslN2ZMCTsOkiooKLBHH53njpILZjnpngumNZxQKGRvvPF7d3RtgwcPsRUrVjAARYfC4XCHdzEVFVUZGYBm5McKgo9CrF+//qrH00Ew9933MysvLyeaa+CTA4nV1NTYpk2bbN++/8/+gruW+fPnW0lJiTuTXhn9eZxgthM8pu7Vq1fb1ovECKdjwVD05MmTVlhYmPE3X36QDRB0679xosfrbOuGKpscf7cM3jEHDJhmVRvet0hr1L0C6ITocavbus6qJg9z19Mwm1y1wd6PtLgXZE83hRO11s9es1kT5tjb/xpvqz5taLvNaPj0ORsded7u/slLVkc86IzWv9uGWdPt/rfP2MRV+y9eTw37bdXow7b07l/Zirp/uxdmSXCr1lUXmt6KzS6+N/bUrqbYBXfusgtfxN6aPTZ2z/KPYqfdKXSsqKjArW5Al66Zp3bEjrW7oM7Fmt4Kx4rveTFWe7rdb2ZMN+w4X9oHq5+z3T9+zB4f37/9FpYzwKY/9rD1WLvVPm5h10FHotbywatWsXuiPfn4BLup3QXVw/pPf8Se6PG2vflxszuXeV0Pp+UT2755oD1RPsby3KlrOvO5HTlx3h0AiTRb3fYPLfTE/XZXXrLL85928MjJeGbZ0cVw4u8OdTttsw21Qf16uHPt5fQbZLfmfmGRplZ3Bkig7Y34nN06qE/iizOnjw26Nc8ikWOWrSuqi+GctxNHPrczoSFW0DvxHxU9ccQOnhlooYLe7gxwbSldK9GTduRgi4VCN1u2rqguhtPD+g0aarnu6Nqi1tp02CK5yXclXO1GHX5evDtxB4m0HovvNnnJd6U06+J/N8d6FwyxUOSwNSV63ByN2OblNTZw1jS7Pek9KxDX++b4TnI8yW39VxbZ/Iq9NnCGld2e785lXpev5JyhE23muJ22dF2tu988b0drqmzOiu0Waf3Kjm552ZZFJticn47I2raK60jOYJs08/u2eemmy7O/6NEamzdnpb0XaYmvt9nzyyI2ZU6p3Zbknwdp5x5Ld8GF2Ol/bIw9VHxvrHLjRxefu58+FNuxfGasuKggVlSUYL4DJHL6k9j6h8bG7qmsjtUeOxc/cSp2aMeL8WssuJ6+l2C+k1ndkGz8dm3YA7Z219M2JnePLbql0AYMn2APrjWb9fxCm3TbDyzELVqn3dA/Adr7Fitf+wd7dsw3bfeiO+Pfi+F294PV8Qvqd7Zg0u32w1DSwUdGpPlDnlFrjWyxJcsareyFR2xUNrfW6wyfjk6g9TOrWfKy1Zc9bQtGfcedzDw+He0pwvEbWwAgIBxAwK0aIGDHAQSEAwgIx1M39BznOkA4gIBwAAHhAALCAQSEAwgYgAICdhxAQDiAgHA8xQDUb4QDCAgHEBAOICAcQMAcBxCw4wACwgEEhAMICMdTDED9RjiAgHAAAeEAAsIBBAxAAQE7DiAgHEBAOJ5ijuM3wgEEhAMICAcQEA4gIBxAwAAUELDjAALCAQSE4ykGoH4jHEBAOICAcAAB4QAC5jiAgB0HEBAOICAcQEA4nmIA6jfCAQSEAwgIBxAQDiBgAAoI2HEAAeEAAsLxFHMcvxEOICAcQEA4gIBwAAHhAAIGoICAHQcQEA4gIBxPMQD1G+EAAsIBBIQDCAgHEDDHAQTsOICAcAAB4QACwvEUA1C/EQ4gIBxAQDiAgHAAAQNQQMCOAwgIBxAQjqeY4/iNcAAB4QACwgEEhAMICAcQMAAFBOw4gIBwAAHheIoBqN8IBxAQDiAgHEBAOICAOQ4gYMcBBIQDCAgHEBCOpxiA+o1wAAHhAALCAQSEAwgYgAICdhxAQDiAgHA8xRzHb4QDCAgHEPBUDRCw4wACwgEEhAMICAcQEA4gIBxAQDiAgHCATjP7H+uV8meCHcl7AAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>Point P is now moved closer to the charges.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A point charge <em>q</em> = −2.0 μC and mass 0.25 kg is placed at P. When <em>x</em> is small compared to <em>d</em>, the magnitude of the net force on <em>q</em> is <em>F</em> ≈ 115<em>x</em>.</p>
</div>
<div class="specification">
<p>An uncharged parallel plate capacitor C is connected to a cell of emf 12 V, a resistor R and another resistor of resistance 20 MΩ.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the resultant electric field at P is 3 MN C<sup>−1</sup></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant electric field at P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why <em>q</em> will perform simple harmonic oscillations when it is released.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the period of oscillations of <em>q</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At <em>t</em> = 0, the switch is connected to X. On the axes, draw a sketch graph to show the variation with time of the voltage <em>V</em><sub>R</sub> across R.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage <em>V</em><sub>c</sub> drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«electric field at P from one charge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>44</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>48</mn><mn>2</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7168</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> «NC<sup>−1</sup>» ✓</p>
<p><br>« net field is » <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>7168</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mi>cos</mi><mo> </mo><mn>30</mn><mo>°</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>97</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> «NC<sup>−1</sup>» ✓</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>directed vertically up «on plane of the page» ✓</p>
<p> </p>
<p><em>Allow an arrow pointing up on the diagram.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force «on <em>q</em>» is proportional to the displacement ✓</p>
<p>and opposite to the displacement / directed towards equilibrium ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mi>a</mi><mo>=</mo><mfrac><mi>F</mi><mi>m</mi></mfrac><mo>=</mo><mo>»</mo><msup><mi>ω</mi><mn>2</mn></msup><mi>x</mi><mo>=</mo><mfrac><mrow><mn>115</mn><mi>x</mi></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>ω</mi></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>29</mn><mo> </mo><mo>«</mo><mtext>s</mtext><mo>»</mo></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreasing from 12 ✓</p>
<p>correct shape as shown ✓</p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><em>Do not penalize if the graph does not touch the t axis.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>20</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo> </mo><mi>C</mi></mrow></mfrac></mrow></msup></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> «F» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.</p>
<p style="text-align: center;"><img 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"></p>
<p>The mass of ions ejected each second is 6.6 × 10<sup><span style="font-size: small;">–6 </span></sup>kg and the speed of each ion is 5.2 × 10<sup><span style="font-size: small;">4</span></sup> m s<sup><span style="font-size: small;">–1</span></sup>. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.</p>
</div>
<div class="specification">
<p>An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.</p>
</div>
<div class="specification">
<p>In practice, the ions leave the spacecraft at a range of angles as shown.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the initial acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Estimate the maximum speed of the spacecraft.</p>
<p>(ii) Outline why the answer to (i) is an estimate.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why scientists sometimes use estimates in making calculations.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ions are likely to spread out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>change in momentum each second = 6.6 × 10<sup>−6</sup> × 5.2 × 10<sup>4</sup> «= 3.4 × 10<sup>−1 </sup>kg m s<sup>−1</sup>» ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}">
<mfrac>
<mrow>
<mn>3.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>740</mn>
</mrow>
</mfrac>
</math></span> =» 4.6 × 10<sup>−4</sup> «m s<sup>−2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>ALTERNATIVE</strong><em><strong> 1:</strong></em></p>
<p>(considering the acceleration of the spacecraft)</p>
<p>time for acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «4.6 × 10<sup>6</sup>» «s» ✔</p>
<p>max speed = «answer to (a) × 4.6 × 10<sup>6</sup> =» 2.1 × 10<sup>3</sup> «m s<sup>−1</sup>» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>(considering the conservation of momentum)</p>
<p>(momentum of 30 kg of fuel ions = change of momentum of spacecraft)</p>
<p>30 × 5.2 × 10<sup>4 </sup>= 710 × max speed ✔</p>
<p>max speed = 2.2 × 10<sup>3 </sup>«m s<sup>−1</sup>» ✔</p>
<p> </p>
<p>(ii) as fuel is consumed total mass changes/decreases so acceleration changes/increases<br><em><strong>OR</strong></em><br>external forces (such as gravitational) can act on the spacecraft so acceleration isn’t constant ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>problem may be too complicated for exact treatment ✔</p>
<p>to make equations/calculations simpler ✔</p>
<p>when precision of the calculations is not important ✔</p>
<p>some quantities in the problem may not be known exactly ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ions have same (sign of) charge ✔</p>
<p>ions repel each other ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the forces between the ions do not affect the force on the spacecraft. ✔</p>
<p>there is no effect on the acceleration of the spacecraft. ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A square loop of side 5.0 cm enters a region of uniform magnetic field at <em>t</em> = 0. The loop exits the region of magnetic field at <em>t</em> = 3.5 s. The magnetic field strength is 0.94 T and is directed into the plane of the paper. The magnetic field extends over a length 65 cm. The speed of the loop is constant.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed of the loop is 20 cm s<sup>−1</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Φ</mi></math> in the loop.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy dissipated in the loop from <em>t </em>= 0 to <em>t </em>= 3.5 s is 0.13 J.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg<sup>−1</sup> K<sup>−1</sup>. Estimate the increase in temperature of the wire.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>70</mn><mrow><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></math> ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>shape as above ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>shape as above ✓</p>
<p> </p>
<p><em>Vertical lines not necessary to score.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>maximum flux at «<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo>×</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>19975</mn><mo>≈</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo> </mo></math>«Wb» ✓</p>
<p>emf = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>20</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>emf induced in one turn = <em>BvL</em> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo> </mo></math>«V» ✓</p>
<p>emf <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0094</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo> </mo></math>«V» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mo>«</mo><mfrac><mi>V</mi><mi>R</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>4</mn></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>33</mn></math> «A» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mo>«</mo><mi>N</mi><mi>B</mi><mi>I</mi><mi>L</mi><mo>=</mo><mn>85</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>94</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>05</mn><mo>=</mo><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn></math> «N» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Energy is being dissipated for 0.50 s ✓</p>
<p><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>F</mi><mi>v</mi><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>13</mn></math> J»</p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>V</mi><mi>l</mi><mi>t</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>33</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>50</mn><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>13</mn></math> J» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)</strong> and <strong>(c)</strong>. </em></p>
<p><em>Watch for candidates who do not justify somehow the use of 0.5 s and just divide by 2 their answer.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>T</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>13</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn><mo>×</mo><mn>385</mn></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>T</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> «K» ✓</p>
<p> </p>
<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Award <strong>[1]</strong> for a <strong>POT</strong> error in <strong>MP1</strong>.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the electric field lines of a positively charged conducting sphere of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="352" height="213"></p>
<p>Points A and B are located on the same field line.</p>
</div>
<div class="specification">
<p>A proton is placed at A and released from rest. The magnitude of the work done by the electric field in moving the proton from A to B is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup><mo> </mo><mi mathvariant="normal">J</mi></math>. Point A is at a distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> from the centre of the sphere. Point B is at a distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> from the centre of the sphere.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the electric potential decreases from A to B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, the variation of electric potential <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> with distance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> from the centre of the sphere.</p>
<p><img style="display: block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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" width="336" height="236"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electric potential difference between points A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math> of the sphere.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The concept of potential is also used in the context of gravitational fields. Suggest why scientists developed a common terminology to describe different types of fields.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 1</strong></em><br></span><span class="fontstyle2">work done on moving a positive test charge in any outward direction is negative </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">potential difference is proportional to this work </span><span class="fontstyle4">«</span><span class="fontstyle2">so </span><span class="fontstyle5"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle2">decreases from A to B</span><span class="fontstyle4">» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 2</strong></em><br></span><span class="fontstyle2">potential gradient is directed opposite to the field so inwards </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">the gradient indicates the direction of increase of </span><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle5">«</span><span class="fontstyle2">hence </span><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle2">increases towards the centre/decreases from A to B</span><span class="fontstyle5">» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 3</strong></em><br></span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>R</mi></mfrac></math> </span><span class="fontstyle3">so as </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> </span><span class="fontstyle3">increases </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle3">decreases </span><span class="fontstyle4">✓<br></span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> </span><span class="fontstyle3">is positive as </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math> </span><span class="fontstyle3">is positive </span><span class="fontstyle4">✓</span></p>
<p><span class="fontstyle2"> </span></p>
<p><span class="fontstyle0"><em><strong>ALTERNATIVE 4</strong></em><br></span><span class="fontstyle2">the work done per unit charge in bringing a positive charge from infinity </span><span class="fontstyle3">✓<br></span><span class="fontstyle2">to point B is less than point A </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">curve decreasing asymptotically for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>></mo><mi>R</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">non <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math> zero constant between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> and </span><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAADWCAYAAACJ36THAAAXiUlEQVR4Ae2dV6xVxduHufHKC70wotEgMSqIvUSNN8RoMIgNFVDshSIgIkVQmkrvWAALYBRFUaQoIEqxYKOIioKABRURRFCailjef37zZfGts88cOLtx9ux5JtnZa89aa++Z513nd6a8804tI0EAAhAIgECtAMpIESEAAQgYYsVDAAEIBEEAsQrCTBQSAhDIS6x27dplkyZNsm3btkESAhCAQFEJ5CxWO3bssB49eliTJk2se/futmXLlqIWlC+HAATiJpCTWEmYevbsaStWrLA+ffrYwoUL7cEHH0Sw4n6WqD0Eikoga7HavXu3jRkzxpYtW+YK1rdvX9u5c6f73L9//6IWli+HAATiJZC1WAmVxqqSlIhVZn5ynncIQAAChSCQk1ilfzgtVul8jiEAAQgUkkDBxOqff/6xLl26uLGr//77r1IZx40bZ61atbI9e/ZUOkcGBCAAgf0RKJhY6Yfmz59vRx55pG3fvr3C70q8GjRoYBMmTKiQzwcIQAAC1SVQULHSWFb9+vVt6tSpFX5/6dKlduihh9rmzZsr5PMBAhCAQHUJFFSs1ILSGFazZs1Ms4ZK//77r3Xo0MHatGlj6iqSIAABCORCoKBipQKsX7/eateubWvWrHHl2bRpkx1++OG2ePHiXMrHPRCAAAQcgYKLlb714osvtn79+rkfmDhxoh177LHghgAEIJAXgaKI1eTJk61hw4a2YcMGtxxnxIgReRWSmyEAAQgURaw0G1ivXj0bOXKk1alTx9atWwdpCEAAAnkRKIpYqUSdO3e2unXrWtOmTfMqIDdDAAIQEIGiiZXcFRo1amRz586FNAQgAIG8CRRNrPIuGV8AAQhAIEUAsUrB4BACEChdAohV6dqGkkEAAikCiFUKBocQgEDpEkCsStc2lAwCEEgRQKxSMDiEAARKlwBiVbq2oWQQgECKAGKVgsEhBCBQugQQq9K1DSWDAARSBBCrFAwOIQCB0iWAWJWubSgZBCCQIoBYpWBwCAEIlC4BxKp0bUPJIACBFAHEKgWDQwhAoHQJIFalaxtKBgEIpAggVikYHEIAAqVLIG+x6tOnj9vUVNtwpV/agiv5XNVx5vn0dTqX/lzVceZ3JPcl1yfvSX7m9b7zytOLBAEIlA6BvMRq48aN1rhxYxs4cKCNHj3atDFE8ho6dKj3eNiwYS5/+PDhe88nebpH+ckrydd3DhkypML1yf3Je/ra5Ht0X5Kv63xlSuclv6H3Tp062erVq0vHUpQEApETyFusLrjgAuvYsaP1799/72vw4MF7j9P5Oh4wYIATt8x8bd119913u/sy78/8nHnvoEGDKvxe165d7aGHHrLM/OQ+iWuPHj2sV69eFe6TQKkcele92rZta7/99lvkjwjVh0BpEMhLrFSF3r1726+//up2W9aOy+nX33//7T5nvifXJPn6rOM9e/Z478+8Prkvec88r+9Jn0uOk3ddn1zjy9u5c6eNHz/errjiCidou3btKg1rUQoIREwgb7HSdvH64y6npPo0a9bMxo4dazfddJONGjXKiVs51ZG6QCA0AoiVx2Lq+kms3nvvPVuwYIG1bNnStHGrWmEkCECgZgggVh7u27ZtsxtuuMEWL17sBGr69Ol29dVX28yZM1031XMLWRCAQJEJIFYewBrTWrFixd7urT5PnDjRrrnmGnvzzTcRLA8zsiBQbAKIVRaENeh+7bXX2pw5cxCsLLhxKQQKQQCx8lD8/fffnX/WqlWrKpzVmNVTTz3lxrBmzJiBYFWgwwcIFJcAYuXhmx5gzzz9119/uS7h9ddfb9OmTUOwMgHxGQJFIoBYecBKrJo3b+5mAz2nbffu3fbMM8+4GcMXX3zRffZdRx4EIFA4AoiVh+X27dutdevWbjbQc9plqUuYzBLKH0v3kCAAgeIRQKzyZLto0SLn1nD//ffbli1b8vw2bocABKoigFhVRSaL/JUrV9ott9ziWmNff/11FndyKQQgUF0CiJWHlLp0t9122z67gZm3ff/9924doVwb5s+fT4iZTEB8hkCeBBArD0ANsLdo0cLUxcsmaUH3uHHj7KqrrnIuDjt27Mjmdq6FAAT2QQCx8sCRWElw3n//fc/ZfWcpmoNcGrQAWiFo1q5d64IQ7vsuzkIAAvsjgFh5CMmXat68efbLL794zlYvS4H77rrrLrv55pvt9ddfZxF09bBxFQSqJIBYVYkm/xMKNTNhwgRr2rSpPfDAAwTyyx8p3xAxAcTKY3w5fc6aNcs2bNjgOZtdlmK+L1u2zNq3b+/WFc6ePZvYWNkh5GoIOAKIledBSMasPvzwQ8/Z3LI02P7YY4/ZddddZz179jS5O7ApRW4suStOAoiVx+5yXVA4GAXfK2RSqJmlS5e6+O8agNei6E2bNhXyJ/guCJQtAcTKY1qJlfylPvjgA8/Z/LMU011LdSRYWtYjvyyNb6nLSIIABPwEECsPF80GfvTRR7Z161bP2cJl/fDDDzZy5EjnJtG9e3c3tkXo5MLx5ZvKiwBiVQL2XLNmjdslSLvpdOvWzZYvX14CpaIIECgtAoiVxx5qWT3xxBN2INf5qUX18ccfOxcHida9997rlvvIyZQEAQiYIVaep0CzgRpgz8WD3fN1WWX98ccfrmXVp08fF5FUovXOO+/sjQef1ZdxMQTKiABi5TFmIlaFdF3w/Mw+syRaamlpZ2nttKPdqrVZxebNmxmI3yc5TpYrAcTKY1nNBt55551OLDynD2iWuoGfffaZDR8+3C2ubteunYtS+u233+JcekAtwY/VNAHEqqYtkMXvf/fdd/b000+7lpacS/v37+9mELXBBW4PWYDk0iAJIFYBmk1dxLlz5zpP+EsvvdTatm1rzz77rH311VdsYBGgPSly9QggVh5O2pFZ0RKK5RTq+cmcsjRrqdaWlvGoe6hdo7t27Wqvvfaabdy4kdZWTlS5qVQJIFYey2iAXX/4NTnA7ilWlVlaY6jAf1oeNHDgQLv11ltNW4Xp+N1337WffvqJdYhV0uNEKAQQK4+lQhOrdBXkr7V+/Xo3c6hNLBSeuVWrVtavXz97++23XSQJfLfSxDgOhQBi5bGUBqxnzpxpiqseclKLS0t6Xn31Vdc91HpHrUeUcCmaqbqKGv9icD5kK8dTdsQqHlu7CA8SLgUCVNhmecrLf0sbtn7++ed0FSN6FkKsKmLlsZqC7ykU8c8//+w5Wx5ZalFpTE7LitTauuyyy1xEU3nOa4BeM4u0uMrD1uVSC8TKY0mNWTVr1iyYAXZPFaqdJUFSeBpFRX3ppZec86k85ps3b2433nijDRgwwLlJqOWleFwkCNQUAcTKQ74Ultt4inVAsjTOpbGsb775xsWP1yC9NnCVeMmfS8t/tFZRXvWagSRB4EARQKw8pJOWVU0sZPYUp0az1PLS7KIinE6ePNnFkr/99ttdy1PipRDNjz/+uH355ZfuOrzpa9RcZf3jiJXHvHK2XLhwYVmPWXmqXe0sCZIcZhMvei39UZQKDdorSsTQoUNt0qRJzmFV25n9+eefbvCeMbBqI+ZCDwHEygOFrOwJKJb8nDlzbMqUKS6AoLYf01IgDdxr/8TRo0e7buUnn3xiCuvMZhnZM479DsTK8wRoNlBdHnV/SNkTkBDJOVXLljSrOn78eOdNr1lHrQy4/PLL3S4/gwYNcpxfeeUVU7RURbtQq5YEAR8BxMpDRWNWahksWrTIc5asXAjIa15c1S1cvHixE7BRo0bZfffd55YGaXmQupNaKqQZSM1MSuiWLFniBvzVGmM2Mhfy5XMPYuWxpf6oNPtV6K24PD8VfZbcJuRlL78urWMcO3as87DXgmwtJpeIScA6dOhgnTt3tjFjxrixMm3ooUF9dT81hoaQlf+jhFh5bKzuSMeOHV2sKM9psg4AAQ3Ka7nTF1984XYaev75553bhMa/tNaxRYsW7qUZSYlYr169bNy4cU7INC4m8VNUVW0uq269xIwB/gNguCL+BGJVRLh8dXEISHy0mYe6k9pz8bnnnnOtsfbt27vAhFdeeaWbmZSgderUyQnZ4MGD3QC/QkPLwVVOsOpa6rs0vqZxNsSsOPYq1LciVoUiyfeUDAF1LT/99FMXZUILtjXAr5aXWmRamaBZyksuucQkanJ41Z6Nw4YNc/5iGivTWKUG/CVoLPQuGbOyu43PFJrFatmyZckH3/OVnbzKBNRiUutJM43qXmpMUuNd8qV7+eWX3fpIhYiWaKlbqeVGEjJNsmixt54FtdAUH0xdTXVJZ82a5Z6P1atXO38yDR0Qeqcy+0Lm0LLy0NTDrP/ApR4p1FN0snIkICHTQH0yY6klR2qdJYImL325WshjX2NkrVu3dq0yzWBqEkCTAfLsVxSLvn37uokAdU9nz57ttnTTOJpaa5pM2LJli/stup3ZGQux8vBKxIrlNh44kWdJ1PR8SMzWrVtnallpKZLcLOQQK1HT+kl58msMTbskaTZT3U35manVpjzNbnbp0sXtxK0u6JNPPulaeRqD0xZsEjbtYCRfP814bt261S04j7n1hlh5/vj0H1a7yOhhzEx6WPSfUf5CybseJHUvSBBIE9AzoWdEralE1NRS0yD/1KlT3YD/iBEjXGBEtcwkanqXoClQot4lcsrXLKgEUC07TRYkKwJeeOEFJ5Rys9FvSET1bOqZ1HCGZkP1PCcTCenyhXaMWGVpMT0Up512mp100kl28sknW/369e3MM8903UY19UkQyJWAWm0SGLWk1LJatmyZvfXWW258TOKmHYw0ZjZkyBDr0aOHG1/TjKfWZGqMTUubtDpAY23qnqpbqlbcPffc47qmEjltLjJx4kS3cmD69On2xhtvuFnVtWvXulacJic0vpe85PKhl2ZLa3rGFLHyPFn6j6jxKv2HykwaXD333HNtxYoVe196qDQwe8YZZ2RezmcIFJ2AWvtqQcmvTKKjf5pqvWlmU1FgNRuq7qlacZpI6Natm9sNSS03CV3jxo3dDGkyS6p35WtiQYLXpk0b16rTyoKkRacur2ZaNdGgLrBajPqbWblypeuRKHBloR11ESvPo6QxCXmwy48nM2kDBu2OnJlkrHr16mVm8xkCNU5AA/l6STzUYlKXUP+Q1T1US0pdRrlpaFs3dSX1z1ctLrXm1ArTqoKRI0e6Fp0mGRTDXy07TSbIHURBGiVuatHppWNF4VCrL5mAUHdWrTw5W0ss9T2PPvqo6wrrdxTBY38JsfIQklhVtRXXKaec4v6bpG/TQKhmhNQMJ0GgHAkkYqeuajJzqi6reh/qtmoiQCsO9LewatUqN5OqiQcFalTLSyGDJE5y/9AeAJoxVWBHvSR8Go/bX0KsPISqEis1s4866ig766yz7MILL9z7Ou+885yTocYZSBCAQPUIJONi6sZqNcH+EmLlIaT/HPJiztwwQuMA55xzjmu6yodmwoQJVrt2bdc8jnlK2YOQLAgUnABilQVS+cJotkX/EZK0YMECO/vss+3HH39MsniHAAQ8BNRd1IykzyXIc3mlLMSqEhJzA5Ca1s0MvqdZEW1VlZlOP/1055eVmc9nCEDg/who0F3DJ/IZu+OOO3KaKUSsPE+Txqw0q5EZfK9BgwY2b968SneoS9iwYUM3fVzpJBkQgIDzTdQgu3olmoXMJSFWHmoSK027ZoqVBEzeyJlJPi6alpXvFQkCEKhMQL0PzQrmk6oUK01VaqmApiHVHZL3qi9pClK+GuWUJFZylMsUq3KqI3WBwIEkIIfp6vhS7atMVYqVujvnn3++HXbYYXbiiSfaI488UmFgOfnSchUrrc0i6kJiZd4hkB+BoomVdtqVN7ZWj8v/QYp48MEH2/LlyyuVuFzFytcNrFR5MiAAgWoRKJpYaSCsUaNGFYKJyeu0Xbt2lQpWjmKllevHHHOMaYsoEgQgkD8BRWaVN3s6KfCh/taqm7zdQDk7aswmnbSAUQHpMlM5ipUG0SVWWrNEggAE8ieg9Ydytk4nxe3q3bt3Jefr9DXpY69YaZV2plg9/PDDbnFi+mYdl6NYSe3r1KmDWGUam88QKDABLZqWYPkinGT+VN5iJScveaVqw8pyeWmsTsto5LxWLnWiHuXzfJabLaUh2tBjf8krVoqBoz6m3BeSNHToUBe1MPmcvCvIvhbwyr2hXF7aTKBJkyY2Y8aMsqlTudiGepTP35lsqf0dFXFBcbH2l7xipY0l5cSVxHOS06Nc5TXwnpnKsRuYOIWyI3OmtfkMgcIRUEwt9cqqI1T6Va9YqUWl7buPOOIIu+iii+zoo492YVMVvyYzlbNY4RSaaW0+Q6BwBMaMGeM2qU334Pb17V6x0g1SPQXPUkB6OYj6hErXIVb7wss5CECgKgKaIaxqZYzvnirFynexLy8tVvphjfeo+6g916oTUMv3nTWdl3QD8WCvaUvw+xD4fwIFEysJlfyzjjvuODftX7duXVO88hAFS4H0VBfFpSZBAAKlQaBgYqX4yyeccIIbLFMfVLtsaFBeXqokCEAAAvkSKJhYaZtszSCmkwLVKWAdCQIQgEC+BAomVvJw1/bY6aStsBWxgQQBCEAgXwIFEyttgKg9xNJpyZIlbjeYdB7HEIAABHIhUDCx0rbU2sgwnbTx56mnnprO4hgCEIBATgQKJlbapkpjVmm/CS1Q7NChQ04F4yYIQAACaQIFEyuFVTn++ONt2rRpbk2hZgMVwG/y5Mnp3+MYAhCAQE4ECiZW+vUpU6bYIYccYrVq1bKDDjrIOnfunNOWOznVhJsgAIGyJlBQsZJ/lbZYVzwobWiYGWyrrElSOQhAoKgECipWRS0pXw4BCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEECswrEVJYVA1AQQq6jNT+UhEA4BxCocW1FSCERNALGK2vxUHgLhEMhbrMKpKiWFAARCJoBYhWw9yg6BiAggVhEZm6pCIGQC/wN+Jc0npxG4UgAAAABJRU5ErkJggg=="></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mi>W</mi><mi>q</mi></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>16</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>60</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> <span class="fontstyle0">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mi>Q</mi><mo>×</mo><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math> ✓</span></p>
<p><span class="fontstyle0"><br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>8</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">C</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">to highlight similarities between </span><span class="fontstyle2">«</span><span class="fontstyle0">different</span><span class="fontstyle2">» </span><span class="fontstyle0">fields </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority who answered in terms of potential gained one mark. Often the answers were in terms of work done rather than work done per unit charge or missed the fact that the potential is positive.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most didn't realise that the key to the answer is the definition of potential or potential difference and tried to answer using one of the formulae in the data booklet, but incorrectly.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Even though many were able to choose the appropriate formula from the data booklet they were often hampered in their use of the formula by incorrect techniques when using fractions.</p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered with only a small number of answers suggesting greater international cooperation.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.</p>
</div>
<div class="specification">
<p>Electricity can be generated using renewable resources.</p>
</div>
<div class="specification">
<p>The voltmeter is used in another circuit that contains two secondary cells.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the emf of the cell.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the internal resistance of the cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the reading on the voltmeter.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Comment on the implications of your answer to (c)(i) for cell B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why electricity is a secondary energy source.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some fuel sources are renewable. Outline what is meant by renewable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.</p>
<p>The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m<sup>−2</sup>.</p>
<p>The overall efficiency of the re-charging process is 18 %.</p>
<p>Calculate the minimum time required to re-charge the cell fully.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why research into solar cell technology is important to society.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>« conservation of » charge ✓</p>
<p>« conservation of » energy ✓</p>
<p> </p>
<p><em>Allow <strong>[1]</strong> max if they explicitly refer to Kirchhoff’ laws linking them to the conservation laws incorrectly.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 V ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>I</em> = 2.0 A <em><strong>OR</strong> </em>12 = <em>I</em> (<em>r</em> + 4) <em><strong>OR</strong> </em>4 = <em>Ir <strong>OR</strong> </em>8 = 4<em>I</em> ✓</p>
<p>«Correct working to get » <em>r</em> = 2.0 «Ω» ✓</p>
<p> </p>
<p><em>Allow any valid method.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Loop equation showing <em><strong>EITHER</strong> </em>correct voltages, i.e., 10 – 4 on one side or both emf’s positive on different sides of the equation <em><strong>OR</strong> </em>correct resistances, i.e. I (1 + 2) ✓</p>
<p>10−4 = I (1 + 2) <em><strong>OR</strong> </em>I = 2.0 «A» seen ✓</p>
<p><em>V</em> = 8.0 «V» ✓</p>
<p> </p>
<p><em>Allow any valid method</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Charge is being driven through the 4.0 V cell <em><strong>OR</strong> </em>it is being (re-)charged ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>is generated from primary/other sources ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«a fuel » that can be replenished/replaced within a reasonable time span</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» that can be replaced faster than the rate at which it is consumed</p>
<p><em><strong>OR</strong></em></p>
<p>renewables are limitless/never run out</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» produced from renewable sources</p>
<p><em><strong>OR</strong></em></p>
<p>gives an example of a renewable (biofuel, hydrogen, wood, wind, solar, tidal, hydro etc..) ✓</p>
<p> </p>
<p><em><strong>OWTTE</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE</strong> <strong>1</strong></em></p>
<p>«energy output of the panel =» <em>Vlt <strong>OR</strong> </em>6 x 5 x 0.25 x 3600 <em><strong>OR</strong> </em>27000 «J» ✓</p>
<p>«available power =» 380 x 0.4 x 0.15 x 0.18 <em><strong>OR</strong> </em>4.1 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>27000</mn><mrow><mn>4</mn><mo>.</mo><mn>1</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«energy needed from Sun =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>v</mi><mi>l</mi><mi>t</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><mn>3600</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>18</mn></mrow></mfrac></math> </strong><strong>OR</strong> </em>150000 «J» ✓</p>
<p>« incident power=» 380 x 0.4 x 0.15 <em><strong>OR</strong> </em>22.8 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>150000</mn><mrow><mn>22</mn><mo>.</mo><mn>8</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong></em></p>
<p><em>Accept final answer in minutes (110) or hours (1.8).</em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>coherent reason ✓</p>
<p>e.g., to improve efficiency, is non-polluting, is renewable, does not produce greenhouse gases, reduce use of fossil fuels</p>
<p> </p>
<p><em>Do <strong>not</strong> allow economic reasons</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) Most just stated Kirchhoff's laws rather than the underlying laws of conservation of energy and charge, basically describing the equations from the data booklet. When it came to guesses, energy and momentum were often the two, although even a baryon and lepton number conservation was found. It cannot be emphasised enough the importance of correctly identifying the command verb used to introduce the question. In this case, identify, with the specific reference to conservation laws, seem to have been explicit tips not picked up by some candidates.</p>
<p>bi) This was probably the easiest question on the paper and almost everybody got it right. 12V. Some calculations were seen, though, that contradict the command verb used. State a value somehow implies that the value is right in front to be read or interpreted suitably.</p>
<p>bii) In the end a lot of the answers here were correct. Some obtained 2 ohms and were able to provide an explanation that worked. A very few negative answers were found, suggesting that some candidates work mechanically without properly reflecting in the nature of the value obtained.</p>
<p>ci) A lot of candidates figured out they had to do some sort of loop here but most had large currents in the voltmeter. Currents of 2 A and 10 A simultaneously were common. Some very good and concise work was seen though, leading to correct steps to show a reading of 8V.</p>
<p>cii) This question was cancelled due to an internal reference error. The paper total was adjusted in grade award. This is corrected for publication and future teaching use.</p>
<p>di) The vast majority of candidates could explain why electricity was a secondary energy source.</p>
<p>dii) An ideal answer was that renewable fuels can be replenished faster than they are consumed. However, many imaginative alternatives were accepted.</p>
<p>ei) This question was often very difficult to mark. Working was often scattered all over the answer box. Full marks were not that common, most candidates achieved partial marks. The commonest problem was determining the energy required to charge the battery. It was also common to see a final calculation involving a power divided by a power to calculate the time.</p>
<p>eii) Almost everybody could give a valid reason why research into solar cells was important. Most answers stated that solar is renewable. There were very few that didn't get a mark due to discussing economic reasons.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.</span></p>
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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The speed of the proton is 2.16 × 10<sup>6</sup> m s<sup>-1</sup> and the magnetic field strength is 0.042 T.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the magnetic force <em>F</em> on the proton.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the velocity vector <em>v</em> of the proton.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">For this proton, calculate, in s, the time for one full revolution.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em>F</em> towards centre ✔</span><span style="background-color:#ffffff;"><br></span></p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em>v</em> tangent to circle and in the direction shown in the diagram ✔<br></span><span style="background-color:#ffffff;"><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><img 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" width="305" height="248"></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> </p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="qvB = \frac{{m{v^2}}}{R} \Rightarrow » R = \frac{{mv}}{{qB}}/\frac{{1.673 \times {{10}^{ - 27}} \times 2.16 \times {{10}^6}}}{{1.60 \times {{10}^{ - 19}} \times 0.042}}">
<mi>q</mi>
<mi>v</mi>
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
<mo stretchy="false">⇒</mo>
<mrow>
<mo>»</mo>
</mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi>q</mi>
<mi>B</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>1.673</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>2.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.042</mn>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><em><span style="background-color:#ffffff;">R = </span></em><span style="background-color:#ffffff;">0.538«m» ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em>R</em> = 0.54«m» ✔</span></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{2\pi R}}{v}/\frac{{2\pi \times 0.54}}{{2.16 \times {{10}^6}}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>R</mi>
</mrow>
<mi>v</mi>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>×</mo>
<mn>0.54</mn>
</mrow>
<mrow>
<mn>2.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = 1.6 \times {10^{ - 6}}">
<mi>T</mi>
<mo>=</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</math></span>«s» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered although usually to 3 sf. Common mistakes were to substitute 0.042 for F and 1 for q. Also some candidates tried to answer in terms of electric fields.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered with many candidates scoring ECF from the previous part.</p>
<div class="question_part_label">bii.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The centre of the ball, still carrying a charge of 1.2 × 10<sup>−6 </sup>C, is now placed 0.40 m from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.</p>
<p>P is the point on the line joining the charges where the electric field strength is zero. The distance PQ is 0.22 m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQoAAABgCAYAAADl0zxBAAAUaklEQVR4Ae2dh7PVxB7H3//xxvcsYAFUnv2JOjbE+gQBxYIIFwU7CIIVBOWigiKoWMDCRQFRioCCoiAXQQRBwV5HQR17b8zo/N58Fn/c3CXJyb3nJOfknN/OZJJsdjfZ72a/+ZXdzT/EgiFgCBgCBRD4R4HrdtkQMAQMATGisJfAEDAECiJgRFEQIktgCBgCRhT2DhgChkBBBIwoCkKU/wQ//PCDDBw4QHba6Z9u69ChnUyefHeLKnbiiSe4MoKZHn30EenU6b/byz3zzF6yadPGYBI7rhIEjCiqpCHjqgFJ0KG1E9PBIY2kZFFfP8alpxwNlEUZw4cPc1GQEUTBfSxUHwK5I4ozTj+9+loh5RqFSRB0arZCYeXKRkcIlBEkCkiGuGDQtOwtZINAVv3BiCKb9izbXfTLv2jRwmbPgJTgd/RmCf4+QeVAavCJAtLgWjAgVYRJKqq2kEfVH1VTgnEqnQTLtON4BIwoIvDJCpiI2+cuGoKgc6raoRVAIiCezh0VIBNVJXyi0M7v5yUd+YKBtNxL41XyIE7VH1WH2FtIjkBW/cEkiuRtksuUSghRROHHayW1M6sa4ROFf675wuIhCiWcYLqwOCUTTWf7eASMKCLwyQqYiNvnLrq1REHnDqoCPgH45wpMWDxlsQVDWLqwuGAeO94Rgaz6g0kUO2JfVTGtUT2CKoeC4XdiOn7QuBlM50sFRhSKTun3RhQRmGYFTMTtcxfdGmMmpID9IGrTcRm+lBBnzPTT+sQDsGFxuQM84wfOqj/kTqLIuB2q4nZ0QDUaaoWSukc1vd+JKY+4YPDtGnrNJApFIr97I4r8tl3iJ8fWgOFQDZfqYfDJI65Anyg++eQTJ3GoHQNpAvLxDZSUaUQRh2w+rlUNUUydOkXeeOONfKCe8VPSqYPjFYJuSR5FVYYwm4M+qk8UxEM0EIOqKDo2QvPo3ohCkWj9fuTIEfLjjz+2voAic+aeKFavXi1dunR2LyvHFgyBakQAMm7Xbk/hg1iOkDuiUOPNli2bpa6u3/avGUAaUZTjFbJ7ZoGASm3s+TDqu679Ie1nyCVR3H77bc0IIgiiHUd7Kwyb6sKGD6URRQRFAgxEgRjmv/jKshFZLdoQyC0C/rvOuRFFTHMqg5rqEQOSXao6BIJEYapHguZVotCkSBFmzFQ0bF+tCEAUSNGzZz/WrIp+f2h2sYQnubRRhNUfAM09GoaMxVUDAqjbYe5RI4qI1s0KmIjbW7QhUFEIZNUfcidRVFQr2cMYAjWCgBFFjTS0VdMQKAYBI4pi0LO8hkCNIGBEUSMNbdU0BIpBwIiiGPQsb8kQYGYrk8p0vAATyQqtn8miPH6esEWEtUz2Otu1ZA9eIwXljiiysvLWSPtXTDWZhUqnZyYrgQ5Nx9ap8f6D6oI8wY6veXSdT2bDBqfXk0fv45eX1/Os+oMRRV7fkCp67qgFb5jaHrVmBqTgL5wDJBAB13S9DD8/5xAQ16shGFFEtGJWwETc3qJTQEA7r0oTegvUj7g1MjRdcB+29kXwuq4hGlRRdD0O1voMqjKc+ypRIXUoeK8sjrPqDyZRZNGado9YBOiQYdIBJEHHb0mgnKA64udVUgpKFEoUSBpKIJqO8lT9UdUmmNcvP+tzI4oIxLMCJuL2Fp0CAhBCFFGExUc9gnZu7dhh6VBNfClFiSIYTxm+8VPjlEzCys86Lqv+YBJF1i1r99sBgVIQBV95SAWyiApIBBCFr+IoUQR/M6CkECwvLC7qXlnFG1FkhbTdp+wIFKt60NHDJIVgxejwQTUieC3PRBGsR5rHuZMo0gTDyi4PAqoy+F967BMYF+MCX/lC6SCioP3BL8+Iwkdkx3Mjih0xsZiMEWiNe5RH1N8OBG0LwUeHACCaKElC0xpRKBLReyOKaGzsSoYIoDq0ZMCVkkScxIGkgSShA7CiqmNEEYVMU7wRRRMWdiSyfXXnrMHAk0Cnp2OzQRzBMQvamVV6UBLQ9ME9EgTlBeP846CRUsuuZGPmkiWLs26SZvfLHVFkZeVthlINnLCk4CGHHCw9e3avgdrmr4oQHW3jr+KWVX+oaKJgAd27775LunfvJvvv/x/3hQAY/ToQ16dPb7eOIGkttBwBcOMFVEyNKFqOYRY5tH3YDx48aPuyeDVNFHzdjjrqSPfytm3bRjp0aC8HHXSgHHPM0e4/Bscd19kd8wXcd9+9hTQACKHYkv3JXlvWXwz7P4oRRTL8sk4VJAqO9a9hNUkUfN2OP76L7LzzvxwQRxxxuHN9ndatmyOIs886y+3P7d1bep9zjuh5t65dpUuX42SffTrIrrvu7AgjbCHSrBu3ku/HYsRh/0bxX0g7r9yfBvGhrDmimD9/nuy22y6y1157CARxyiknS68zzpC+550nAwcMkEsvuUQGXX65A2bIFVfIFYMHu3PiB1xwgZzXp4+7dsIJx8uee+4ubdrsatJFAaaCTPn5bZAMTKIoAFqZLgfbCIJHGiTUFFE0NEyTXXb5t3TsuK+TKE7v2VP69e0rl1x8sQwdMkSuveYauWHkSLnpxhsdMGPr66V+zBi5cfRoF3/N1VcL5HHxRRc5YunZo4ccfPBBrgNQtoV4BIJ2CiOKeKzKdVWJImif4FlqhiiUJA48cH85+eST5Jyzz5YLBw50BDHi+usdIYwfN04m3nGH3HXXnQ6YeyZPdmP677xzktwxYYJwfcxNN8n1113nCAMJBLUEmwYEhLRioTACuOCQMCxUHgL8PjDM/lYTRIGrB6Y84ID9nKqB7QFVAgkB6eG228Y7cpgy5X556KEHZXpDgzzyyHTnX2fPOfH333+fSzd+/DgnZVw1fLiTRrBjdOp0qFNpfLdS5b0K9kSGQOUiUDb3KPpx+/Z7Sfv27eSkk050xsnLLr1Urrv2Whk7tl4mTZwoEETDtGkya+ZMeeLxx2XevLny5Pz527e5c+e4+JkzZsi0aQ87wkDyQDWBbFBdkFAgokMPPaRyW8GezBCocATKRhSjRo2U3XdvI507Hytn9url7AvYIm4eO9ZJBw88MFVmzHhU5s6ZIwsXLJCnn3pKlixeLM8sWSLPPvOM23NO/IInn5Q5Tzzh0pNv0qSJjmyuvuoquejCC51RFOOm2Sua3kYkOQuGQFIEykIUSBN4OPjS4/q84PzzZfiwYU4SwO7w4IMPyKxZM2X+vHmOCCCGZc8/LyteeEEaGxtlZWOj27+wfLk8/9xzjjQgDCQOpA9HFhMnOrvFlUOHSv+6Ojn22GNCF0dJClS1pTOiqLYWTbc+ZSEKvuxIE4x9wI6A23PUDTc4wySdnM6OioHE8NzSpdK4YoW8tHq1rF271hkz169fL6+88oo7x8DD9aVLl8rip5925IIqgtqCCwlvyeWXXeaMm23b7iblHjOfbnMmL92IIjlWlZyyqo2ZjLpkcBQDpRgDgYpw6y23yD33THbGSiQDOj3SwosrVzpCePXVV+X11193RPH222/Lm2++6c6Jh0CQMiAV8mG7mD69QfCOoMogrZzfv7+zU3Tt+r9KbvfMns2IIjOoU71RVRMFL+mRRx7hbBMYMPnq4+ZE5Xh89mxZtHChLH32Wdf5161dKxs3bhTI4YMPPnBE8fHHH8tHH30k77//vovnOmSBWoKasnDhAnnssVlOBZkw4XYZOWKEM2xCTNgqLIjzNhkO+UUAyZgxFRAFLu205zplrnqgKuyxR1s3sKrPuee6cQ8MnmLaL1IA0gQqB/aHNWvWOJJ45513HDFs2bLFAfPFF1/I559/LpxDGJDIa6+9JmteekmWL1/u8jupoqHBGUYZYzF40CCn5jDE21ylRhT5pQhxBMHHlg2iYM9ozTTV6syJgjkGTOJicBVGRsY8oHbcd9+9zjaBhwOpAJUDWwQqxocffiifffaZfP311w4Y1g/47rvv5KuvvpJPP/3UXafzY7dABSE/nhC8Jvfee49TP4ZdeaUb7YlLNmzgSp5fnNY8Oy+XhfwhQP9RkggShZJFWnOcMicKDIywX9dTT3X2CVyiDJSaOnWKmy7+1KJFztZAZ0ZKePfdd91fnb788ku3ejIM+vvvv8uvv/4q33//vRCPKoLUgb1i1apVzrCJ+oLnBKPmuFtvdXYQ7BTMJUmTefPy6hlR5KWlmj8nQ+yjiIJ4iCSNkIgogg+W9DjqYZUocIsy1Jph18Th7cA+gZsTVyhqBLaH9957z6kY33zzjfz8889Oovjrr79k69at8tNPPzkpAxWEdKTHO4IRFMLBTgEBQUQQEm5YpqsnqUPU84fFJynPTxNWTlScnzfJeVRZGk8ZGpKU56fRvEn2ft4k50nK1TRJyvPTaN4kez9vkvMk5WqaJOVFpVHVQ6/Tl/yg11qy98tIRBR+pmLOiyUKCOLPP/+UrX/8sZ0oNm/e7IgCCaQQUaStyxWDTZZ5eWks5A8B5nzEdfi0pOXMiQLRiMFWYaoHEgAqA25OVA9UCVQKfu6CioGq8csvv8hvv/3mpAvsFBg2UT0waG7YsGG76oHnA9WDeSCqemATYT1Fs1GYMTN/FLHtiXl3o4iC9SnSCpkTBRXFRYkxs65fP2fMvOXmm50xk4FSaszEKIlxUo2ZGC0hC8iB7dtvv3XnqB24TTFmrlu3bruLVI2ZjM1gLAXGTNa2gKTSdiWl1VilLNckilKimW1ZqNM+WSApp+nNy5wogJRKHn30UcJsUdaRwD3K2pjMBsWtiXsUNyd2CtQJpAU8H5ACblHdUDmI5zrSB2rHsmXLtrlH58xxE8oYEs5MVNyjNo6i6YU2omjCIo9HfOxQ49mQ0tPydig2ZSEKRkcyz4MVrJhWzoArBkZh0KTSqB+4OBlAxUAqjJRvvfWWs0NADIydYI8Bk3jI5OWXX3ZDud2AqwXb1A6YFyBZ14JFbVjMpn//Oq17Te+NKGq6+Vtc+bIQBWTAvAvsFLgsGUuBesCQawZdIVXg/WD+BioIJLBh/XrZtGmTE69QRxCzIBDiGZgFqZCefMwkZXo6UgpT1lE7UHO4p9kntr0jRhQt7is1naEsRAHi2CkOO6yTWy+CSVtIFXz9GffAQCmd78FQbmaNMj4CQmBIN7YI9pyvevFFN4qTdJAEJMOPYzBisvANw7eRWpjO3rHjPjXd2MHKG1EE0bDjQgiUjSj42mNYxG6AN4Lp4Ay1ZsEaVBAMm5AF4yFYgwJPCHYLN9V8xQq35xwpguuoK5AEJIPKwQI2rKnJmpvYQlgSLy3XUSGQK/G6EUUltkryZ9K/s9OObPw5LfhnteQlJUtZNqLg8Vh1ilmkDBphnUxmkbI6FQvPQBZUnJWtmHIOYWDkZIMY2DNTFILgOoO1WB4PiQSSwECKSsOgLuwh/AbAgiGQdwSYvgApsPHbRA0QB79h1F8uanyp9mUlCuwMSBX4f1kMl6XrWMKOTs5sUuZpPPzwQ05KwK7BaldIGbphiyAeQmHtTFyhGEWRTCAJVrdiwRrUnLStwqVqECvHEIhDACKAJMIC440YJxT8r2pYutbElZUoeGAdQIJ0wfqWeCdYP2L0qFFuoBTSBYSBhAFp4ELVjXPiuY7KwuQyFsDBeImEgl0CIkrTv9wa0MuRJ+6nvfwcmJfMQmUjsGnTRqdmxKkYw4cPc5JFqWtSdqKgQqx4RYfGfcn6mSxmw7gHFtrFzsCALAydkAHjIli2nz3nxHMdYmE+B6tl4UnBUGok0fS6KFEExVWuIspCFIitFiobASQF7BFxpK7tvHJlY0krUxFEQY346jMFnLUq+EsYa1UgFUAYqBGMhUBagDgYQKU//2FSGdchCOwR3U87Tfbeu72zf5gk0fSu6AvkEwUpeKl4AeO+VE0l2VG5EKivH1Nw3VeVOsLauZjnrhiioBLYEYYOHeJeWn4+rMv44xXB3sBqWBCCbrg9IROuMxt1v/22/fF89OhRZpPw3oo4okCqgCjS0G29x7DTIhAwovDAY3hqXV1fZ4Rk/QgIgHU2MeJAHswTYc+fwPjDGAOpMFhCMjaPwwPz79M4ojCJIhyzSos11SOmRRj7wD9AcG8efninZluPHt0F6cFGW8YA+PelKKJA31V3W+FSLEU5EVC1Ik5FROooZMdoTR0qSvVoTQUsTzIElCh4ifwNSznqh4XKRwD3KIbnYHvhEsUgTRtznMZYCiOKyn83SvKEShTsLeQXAQhCJUBtS6RCyIMPAEQR5xVpbc3LThRUGnGpUFCRSr+GfAVLERDjYGMtN60BK6V41mLKMKIoBr3Ky4u9QslB310kCY5VuijlU5eVKLRihYhCxS10NAJ7QAKQYgLl+sRAhypF2cU8Vxp5jSjSQLXyykTioD+VWqooC1FQCTo5X3MYMI4oSEsa33WXxAIc14yaP2xginYq/55x5VX6Na0TewuGQEsRSI0o+CqHdUIeEHWDTgj7FSKKqAoV++IXkhp4vmrqVMXiFdUOFl8bCJSFKJRAiiEKlQh8EQvbBeQTDH5clJQSzGPHhoAh0IRAWYhCb18MUSARYGPwg08KXPfjkvij/XLt3BCoZQRySRR0fIgCovGDTwpc9+OMKHzU7NwQiEegZERBx0Xkj9t8NaE1EgUqB54K9YD41fNJget+nN6XsiwYAoZAYQRKRhT+rSAOtUX41/RcO2yc10PTsicdRBRnZPRJgXxhcRhU49yrkJoRSRB9O65lBHJBFBAKnTpOktBGVFIgjwaN03P2agwNIzNIAqJLSmDBcu3YEKhGBHJBFHz9kSTCOrXfKEoKKg2wh2DI70sJYQOuGNsBSXBPC4aAIbANgYokClUxsEOo/z/K9qGEoA0KUSgx0OHp+BAM+cMkEvIrEWkav0wt2/aGQK0ikBpRlAtQiAJysGAIGAKlQ6DqiALpwCSC0r0gVpIhAAJVRRTqRTGisJfbECgtAlVFFECDHcJUj9K+JFaaIVB1RGFNaggYAqVHwIii9JhaiYZA1SFgRFF1TWoVMgRKj8D/AWMjy5YLt6hYAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge per unit area on the surface of the wall is<em> σ</em>. It can be shown that the electric field strength <em>E</em> due to the charge on the wall is given by the equation</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mi>σ</mi><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac></math>.</p>
<p>Demonstrate that the units of the quantities in this equation are consistent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.</p>
<p>Determine the horizontal force that acts on the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge on the ball is 1.2 × 10<sup>−6 </sup>C. Determine <em>σ</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread breaks. Explain the initial subsequent motion of the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the charge on Q. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, without calculation, whether or not the electric potential at P is zero.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies units of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>C</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>×</mo><mfrac><mrow><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><msup><mi>C</mi><mn>2</mn></msup></mfrac></math> seen and reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>N C</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <strong>✓</strong></p>
<p> </p>
<p><em>Accept any analysis (eg dimensional) that yields answer correctly</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on ball <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>T</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>30</mn></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>cos</mi><mo> </mo><mn>30</mn></mrow></mfrac></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo> </mo><mo>«</mo><mo>=</mo><mi>m</mi><mi>g</mi><mo> </mo><mi>tan</mi><mo> </mo><mn>30</mn><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mo> </mo><mn>9</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>×</mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>»</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>14</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow g = 10 N kg<sup>−1</sup></em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer.</em></p>
<p><em>Award <strong>[1max]</strong> for an answer of zero, interpreting that the horizontal force refers to the horizontal component of the net force.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>»</mo></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>85</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em> <br>Allow <strong>ECF</strong> from the calculated F in (b)(i)</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal/repulsive force and vertical force/pull of gravity act on the ball <strong>✓</strong></p>
<p>so ball has constant acceleration/constant net force <strong>✓</strong></p>
<p>motion is in a straight line <strong>✓</strong></p>
<p>at 30° to vertical away from wall/along original line of thread <strong>✓</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>Q</mi><mrow><mn>0</mn><mo>.</mo><msup><mn>22</mn><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>18</mn><mn>2</mn></msup></mrow></mfrac></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>+</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><mtext>C</mtext><mo>»</mo></math><strong>✓</strong></p>
<p>2sf<strong> ✓</strong></p>
<p><em><br>Do not award <strong>MP2</strong> if charge is negative </em></p>
<p><em>Any answer given to 2 sig figs scores <strong>MP3</strong></em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>work must be done to move a «positive» charge from infinity to P «as both charges are positive»<br><em><strong>OR</strong></em><br>reference to both potentials positive and added<br><em><strong>OR</strong></em><br>identifies field as gradient of potential and with zero value <strong>✓</strong></p>
<p>therefore, point P is at a positive / non-zero potential<strong> ✓</strong></p>
<p><em><br>Award <strong>[0]</strong> for bald answer that P has non-zero potential</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch S is initially open. Calculate the total power dissipated in the circuit.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch is now closed. State, without calculation, why the current in the cell will increase.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch is now closed. <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Deduce the ratio }}\frac{{{\text{power dissipated in Y with S open}}}}{{{\text{power dissipated in Y with S closed}}}}">
<mrow>
<mtext>Deduce the ratio </mtext>
</mrow>
<mfrac>
<mrow>
<mrow>
<mtext>power dissipated in Y with S open</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>power dissipated in Y with S closed</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</span></p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Calculate the energy stored in the capacitor.</span></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the change in the energy stored in the capacitor.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suggest, in terms of conservation of energy, the cause for the above change.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">dii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">total resistance of circuit is 8.0 «Ω» ✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = \frac{{{{12}^2}}}{{8.0}} = 18">
<mi>P</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.0</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>18</mn>
</math></span>«W» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">«a resistor is now connected in parallel» reducing the total resistance<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">current through YZ unchanged and additional current flows through X ✔</span></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">evidence in calculation or statement that pd across Y/current in Y is the same as before ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">so ratio is 1 ✔</span></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = «\frac{1}{2}C{V^2} = \frac{1}{2} \times 6 \times {10^{ - 6}} \times {12^2} =» 4.3 \times {10^{ - 4}}">
<mi>E</mi>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>6</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>12</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>4.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{J}}">
<mrow>
<mtext>J</mtext>
</mrow>
</math></span>» ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><em><strong><span style="background-color:#ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">capacitance doubles and voltage halves ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">since <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}C{V^2}">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> energy halves <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">so change is «–»2.2×10<sup>–4 </sup>«J» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"> </span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="E = \frac{1}{2}C{V^2}{\text{ and }}Q = CV{\text{ so }}E = \frac{{{Q^2}}}{{2C}}">
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>C</mi>
<mrow>
<msup>
<mi>V</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mtext> and </mtext>
</mrow>
<mi>Q</mi>
<mo>=</mo>
<mi>C</mi>
<mi>V</mi>
<mrow>
<mtext> so </mtext>
</mrow>
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>Q</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>C</mi>
</mrow>
</mfrac>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span> </span><span style="background-color:#ffffff;"><br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">capacitance doubles and charge unchanged so energy halves ✔<br></span></p>
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">so change is <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">»</span>2.2 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 10<sup><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−</span>4 </sup>«<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">J</span>» ✔</span></p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;">it is the work done when inserting the dielectric into the capacitor ✔<br></span></p>
<div class="question_part_label">dii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates scored both marks. ECF was awarded for those who didn’t calculate the new resistance correctly. Candidates showing clearly that they were attempting to calculate the new total resistance helped examiners to award ECF marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most recognised that this decreased the total resistance of the circuit. Answers scoring via the second alternative were rare as the statements were often far too vague.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few gained any credit for this at both levels. Most performed complicated calculations involving the total circuit and using 12V – they had not realised that the question refers to Y only.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most answered this correctly.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>By far the most common answer involved doubling the capacitance without considering the change in p.d. Almost all candidates who did this calculated a change in energy that scored 1 mark.</p>
<div class="question_part_label">di.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few scored on this question.</p>
<div class="question_part_label">dii.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment a beam of electrons with energy 440 MeV are incident on oxygen-16 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>O</mtext><mprescripts></mprescripts><mn>8</mn><mn>16</mn></mmultiscripts></mfenced></math> nuclei. The variation with scattering angle of the relative intensity of the scattered electrons is shown.<br><br></p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify a property of electrons demonstrated by this experiment.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy <em>E</em> of each electron in the beam is about 7 × 10<sup>−11 </sup>J.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The de Broglie wavelength for an electron is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>E</mi></mfrac></math>. Show that the diameter of an oxygen-16 nucleus is about 4 fm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the result in (a)(iii), the volume of a tin-118 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Sn</mtext><mprescripts></mprescripts><mn>50</mn><mn>118</mn></mmultiscripts></mfenced></math> nucleus. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wave properties ✓</p>
<p><em><br>Accept reference to diffraction or interference.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>440 x 10<sup>6</sup> x 1.6 x 10<sup>-19</sup> <em><strong>OR</strong> </em>7.0 × 10<sup>-11</sup> «J» ✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></math> <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>440</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math> <em><strong>OR </strong> </em>2.8 × 10<sup>-15 </sup>«m» seen ✓</p>
<p>read off graph as 46° ✓</p>
<p>«Use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mi>λ</mi><mrow><mi>sin</mi><mi>θ</mi></mrow></mfrac></math>=» 3.9 × 10<sup>-15</sup> m ✓</p>
<p> </p>
<p><em>Accept an angle between 45 and 47 degrees.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>∝</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>∝</mo><mi>A</mi></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><mfenced><mfrac><msub><mi>A</mi><mrow><mi>S</mi><mi>n</mi></mrow></msub><msub><mi>A</mi><mi>O</mi></msub></mfrac></mfenced><msubsup><mi>r</mi><mi>O</mi><mrow><mo> </mo><mn>3</mn></mrow></msubsup></math> or equivalent working ✓</p>
<p>2.3 to 2.5 × 10<sup>-43 </sup>«m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><msub><mi>R</mi><mtext>o</mtext></msub><mo>×</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><msup><mi>R</mi><mn>3</mn></msup></math> <em><strong>OR</strong> </em>5.9 x 10<sup>-15</sup> seen ✓</p>
<p>8.5 × 10<sup>-43</sup> «m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em>Although the question expects candidates to work from the oxygen radius found, allow <strong>ALT 2</strong> working from the Fermi radius.</em></p>
<p><em><strong>MP4</strong> is for any answer stated to 1 or 2 significant figures.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>ai) Well answered.</p>
<p>aii) Well answered.</p>
<p>aiii) This was generally well done but quite a few attempted the small angle approximation. Probably worth a mention in the report.</p>
<p>b) Most gained credit from the first alternative solution, trying to use the data as the question intended. There were the inevitable slips and calculator mistakes. Most got the fourth mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A negatively charged thundercloud above the Earth’s surface may be modelled by a parallel plate capacitor.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.28.35.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/08"></p>
<p>The lower plate of the capacitor is the Earth’s surface and the upper plate is the base of the thundercloud.</p>
<p>The following data are available.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{Area of thundercloud base}}}&{ = 1.2 \times {{10}^8}{\text{ }}{{\text{m}}^2}} \\ {{\text{Charge on thundercloud base}}}&{ = -25{\text{ C}}} \\ {{\text{Distance of thundercloud base from Earth's surface}}}&{ = 1600{\text{ m}}} \\ {{\text{Permittivity of air}}}&{ = 8.8 \times {{10}^{ - 12}}{\text{ F }}{{\text{m}}^{ - 1}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Area of thundercloud base</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>1.2</mn>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Charge on thundercloud base</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>25</mn>
<mrow>
<mtext> C</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Distance of thundercloud base from Earth's surface</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>1600</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Permittivity of air</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>8.8</mn>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>12</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mtext> F </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="specification">
<p>Lightning takes place when the capacitor discharges through the air between the thundercloud and the Earth’s surface. The time constant of the system is 32 ms. A lightning strike lasts for 18 ms.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the capacitance of this arrangement is <em>C </em>= 6.6 × 10<sup>–7</sup> F.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate in V, the potential difference between the thundercloud and the Earth’s surface.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate in J, the energy stored in the system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that about –11 C of charge is delivered to the Earth’s surface.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in A, the average current during the discharge.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one </strong>assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>C</em> = <strong>«</strong><em>ε</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{A}{d}">
<mfrac>
<mi>A</mi>
<mi>d</mi>
</mfrac>
</math></span> =<strong>»</strong> 8.8 × 10<sup>–12</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.2 \times {{10}^8}}}{{1600}}">
<mfrac>
<mrow>
<mn>1.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1600</mn>
</mrow>
</mfrac>
</math></span></p>
<p><strong>«</strong><em>C</em> = 6.60 × 10<sup>–7</sup> F<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{Q}{C}">
<mfrac>
<mi>Q</mi>
<mi>C</mi>
</mfrac>
</math></span> =<strong>»</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{25}}{{6.6 \times {{10}^{ - 7}}}}">
<mfrac>
<mrow>
<mn>25</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><em>V</em> = 3.8 × 10<sup>7</sup> <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>E</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>QV</em> =<strong>»</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 25 × 3.8 × 10<sup>7</sup></p>
<p><em>E</em> = 4.7 × 10<sup>8</sup> <strong>«</strong>J<strong>»</strong></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><em>E</em><em> = </em><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>CV</em><sup>2</sup> =<strong>»</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 6.60 × 10<sup>–7</sup> × (3.8 × 10<sup>7</sup>)<sup>2</sup></p>
<p><em>E</em> = 4.7 × 10<sup>8</sup> <strong>«</strong>J<strong>»</strong> / 4.8 × 10<sup>8</sup> <strong>«</strong>J<strong>»</strong> if rounded value of V used</p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from (b)(i)</em></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Q</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{Q_0}{e^{ - \frac{t}{\tau }}}">
<mrow>
<msub>
<mi>Q</mi>
<mn>0</mn>
</msub>
</mrow>
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mfrac>
<mi>t</mi>
<mi>τ</mi>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span> =<strong>»</strong> 25 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{e^{ - \frac{{18}}{{32}}}}">
<mrow>
<msup>
<mi>e</mi>
<mrow>
<mo>−</mo>
<mfrac>
<mrow>
<mn>18</mn>
</mrow>
<mrow>
<mn>32</mn>
</mrow>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><em>Q</em> = 14.2 <strong>«</strong>C<strong>»</strong></p>
<p>charge delivered = <em>Q</em> = 25 – 14.2 = 10.8 <strong>«</strong>C<strong>»</strong></p>
<p><strong>«</strong>≈ –11 C<strong>»</strong></p>
<p> </p>
<p><em>Final answer must be given to at least 3 significant figures</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>I</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta Q}}{{\Delta t}} = \frac{{11}}{{18 \times {{10}^{ - 3}}}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>Q</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>11</mn>
</mrow>
<mrow>
<mn>18</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> ≈ 610 <strong>«</strong>A<strong>»</strong></p>
<p> </p>
<p><em>Accept an answer in the range 597 </em>− <em>611 </em><strong>«</strong><em>A</em><strong>»</strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the base of the thundercloud must be parallel to the Earth surface</p>
<p><strong><em>OR</em></strong></p>
<p>the base of the thundercloud must be flat</p>
<p><strong><em>OR</em></strong></p>
<p>the base of the cloud must be very long <strong>«</strong>compared with the distance from the surface<strong>»</strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable.</p>
<p>The following data are available:</p>
<p style="padding-left: 120px;">Length of cable = 10 m<br>Cross-sectional area of cable = 6.0 mm<sup>2</sup><br>Resistivity of copper = 1.7 × 10<sup>–8</sup> Ω m</p>
</div>
<div class="question">
<p>Calculate the power dissipated in the cable.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>power = «35<sup>2</sup> × 0.028» = 34 «W»</p>
<p> </p>
<p><em>Allow 35 – 36 W if unrounded figures for R or I are used.</em><br><em>Allow ECF from (a)(i) and (a)(ii).</em></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">X has a capacitance of 18 μF. X is charged so that the one plate has a charge of 48 μC. X is then connected to an uncharged capacitor Y and a resistor via an open switch S.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" src="data:image/png;base64,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" width="254" height="182"></span></p>
</div>
<div class="specification">
<p>The capacitance of Y is 12 μF. S is now closed.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, in J, the energy stored in X with the switch S open.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Calculate the final charge on X and the final charge on Y.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Calculate the final total energy, in J, stored in X and Y.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Suggest why the answers to (a) and (b)(ii) are different.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>C</mi></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mi>Q</mi><mi>C</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mo>«</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><mfenced><mrow><mn>48</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced><mrow><mn>18</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>6</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math><span style="background-color: #ffffff;">✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mi mathvariant="normal">X</mi></msub><mo>+</mo><msub><mi>Q</mi><mi mathvariant="normal">Y</mi></msub><mo>=</mo><mn>48</mn></math> ✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>Q</mi><mi mathvariant="normal">X</mi></msub><mn>18</mn></mfrac><mo>=</mo><mfrac><msub><mi>Q</mi><mi mathvariant="normal">Y</mi></msub><mn>12</mn></mfrac></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<p>solving to get <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mi mathvariant="normal">X</mi></msub><mo>=</mo><mn>29</mn><mo> </mo><mo>«</mo><mi>μ</mi><mi mathvariant="normal">C</mi><mo>»</mo><mo> </mo><mo> </mo><msub><mi>Q</mi><mi mathvariant="normal">Y</mi></msub><mo>=</mo><mn>19</mn><mo> </mo><mo>«</mo><mi>μ</mi><mi mathvariant="normal">C</mi><mo>»</mo></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn><mo>=</mo><mn>18</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>+</mo><mn>12</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>⇒</mo><mi>V</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math>✔</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mi mathvariant="normal">X</mi></msub><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>18</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>29</mn><mo> </mo><mo>«</mo><msub><mi>Q</mi><mi mathvariant="normal">X</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>18</mn><mo>=</mo><mn>29</mn><mo> </mo><mo>«</mo><mi>μ</mi><mi mathvariant="normal">C</mi><mo>»</mo></math> ✔</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Q</mi><mi mathvariant="normal">Y</mi></msub><mo>=</mo><mo>«</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><mn>12</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>19</mn><mo> </mo><mo>«</mo><mi>μ</mi><mi mathvariant="normal">C</mi><mo>»</mo></math> ✔</p>
<p> </p>
<p><em>NOTE: Award <strong>[3]</strong> for bald correct answer</em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span style="background-color: #ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p><em><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">T</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><msup><mfenced><mrow><mn>29</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup><mrow><mn>18</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><msup><mfenced><mrow><mn>19</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup><mrow><mn>12</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac></math></span></strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><em><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math><strong style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</strong></span></strong></em></p>
<p> </p>
<p><span style="font-size: 14px;"><strong><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">ALTERNATIVE 2</span></span></em></strong></span></p>
<p><span style="font-size: 14px;"><strong><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi mathvariant="normal">T</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>18</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>6</mn><mn>2</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>12</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><msup><mn>6</mn><mn>2</mn></msup></math> <strong style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</strong></span></span></em></strong></span></p>
<p><span style="font-size: 14px;"><strong><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>3</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math><strong style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</strong></span></span></em></strong></span></p>
<p> </p>
<p><span style="font-size: 14px;"><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">NOTE: Allow ECF from (b)(i)<br>Award <strong>[2]</strong> for bald correct answer<br>Award <strong>[1]</strong> max as ECF to a calculation using only one charge</span></span></em></span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">charge moves/current flows «in the circuit» ✔<br>thermal losses «in the resistor and connecting wires» ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept heat losses for MP2</span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A conducting sphere has radius 48 cm. The electric potential on the surface of the sphere is 3.4 × 10<sup>5</sup> V.</p>
</div>
<div class="specification">
<p>The sphere is connected by a long conducting wire to a second conducting sphere of radius 24 cm. The second sphere is initially uncharged.</p>
<p style="text-align: center;"> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAACJCAYAAAARxi7fAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABuqSURBVHhe7d0LVFV1vgfw7zDdatRIJcWKEFEGhQlRE0uqidKRBcYlnVFztLDUNWaROq6r+Gi1MkHnusBIskEnyczXDeVSsnyGo6KFiaRLlPCBpAaaqYRO0yru3b8/e8vxRXA4j70P30/LBXtz2GefveP/2//f//Wr/9OAiIjIwbz0r0RERA7FAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7BAENERE7RIkfyl5WV4dy5czh79ixKS0tx6dIltX/FiuXqa0NiY59Gu3btcPfddyM4OBgdO3ZEhw4dEBQUpL+CiIiExweY7777DkeOHMGXX36JAwcOYMOGj/Hww/3RrVs3REREoE2b1ujcOUC91s/PD7/5zW/U9zfzr3/9C6dOnVLfnzxZjpqayypAlZeXXz1uVFSUFmy6oUePENx///3qtURELZFHBhgJJgcPHkRubi6qqioRExOrahuhoaFOrWlIzUgCz759RcjL2wBf304q4PTv3x89e/bUX0VE1DJ4TIA5ffq0CiirV69SBXtcXBz69evn1tSVnFN+fv7VQDdixLMYMGAA02lE1CJYOsBIyqqgYBcyM5eoAnzcuPGqxmDG1JRtsBHjx49DZOSjDabkiIiszJIBRgLLpk2bkJaWqgrpwYMHqzSUVUgKb82aNSo4Sq1m+PDhaN++vf5TIiLPYKkAYwSWxMSXMXHiKxgyZIil001GWi8lZS6SkmYy0BCRR7HEOBgJLDk5OYiOHoTCwkIUFx/AtGnTLN+WIam8CRMmqM8jnnkmXn1O+bxERFZn+hqMpJPmzp0LHx8fTJkyxaMbyKUX2rJly3D06FHMnDmTPc+IyNJMG2DkKT49PV119509ezYGDBio/8Tz7d69G0lJ01X70tSpU5k2IyJLMmWKTGotkg4TGzdualHBRUiHBfncMluApM0k4BARWY2pajBSa8nKylJjWdLT32aKSCPBNjHxFTVYNDExkd2aicgyTFODkSldpI1FpnNZvz6HwUUn10FqMzJfmlwf6XlGRGQFpggw0rgtqaCwsDAsXryYbQ7XkVpLcnIyIiMjMXLks6pWQ0Rkdm5PkUn7wogRw7B69VpLDZZ0F6MDQErKPF4vIjI1twaYrVu3YM6cOVi69B+cn6sJJE0mNRmZBUDG0RARmZHbAoykwqQxf+XKVZzW3g4MMkRkdm5pg2FwaT65btL4L50i5HoSEZmNywPMihUrGFwcRBr/U1NTGWSIyJRcGmCkgXrJkkwGFweSIDNr1iwVtGUeMyIis3BZgDF6PzG4OJ5cT7musnwBR/0TkVm4pJHfaJBm11rnkvFETz0VhW3b8tkrj4jczuk1GJn+ZfLkydq/KQwuTiZBRcYTjR37opoZgYjInZxeg5kxY4aatFHWbyHXkAZ/NvwTkbs5tQYjjc6ytolM0kiuk5CQoL5Kjz0iIndxWg1G2l0eeaQf9uz5nI36bmC0e3GWBCJyF6cFGBldPmjQIMTHx+t7yNVkKp7MzCV4//33Oc0/EbmcU1JkxngMBhf3koXaunXrhuzsbH0PEZHrOLwGI72XwsPD2FXWJIz7wVQlEbmaw2swCxYsQHLyPAYXk5C1ddLTFyEjI0PfQ0TkGg4NMDLQr6BgF4YOHarvITOQtjC5L1yojIhcyaEpMhnzEhERwbYXE5IpZBYuXIi1a9fqe4jI7KQ36OHDJaisrEJJSYka9vHZZzdOBxUb+zTatWuHkJAQBAYGonv37qZYGdhhAcYowNhjybyGDRuGSZMmcUYFIhOTTNDWrVvVBLYiJiYWwcHBCA0NRatWrW7aliq/c+XKFZw4cQKlpaXIy9sAX99OiIuLQ1RUlNvaXx0WYKRb8ujRo1l4mRhrMUTmZfx9CkcEBkmJyzElUEVGPorBgwe7vHx2SICR6CnzX/3znzv0PWRWrMUQmYsRWHx8fJzykC7zQe7fv/9q8Jo7d67LOmE5JMCw7cU65H/mTz75BMnJyfoeInIHGUIgvW6lXcVVD30y+HrOnDkq7SZTeDm7OaPZvcjkIq1YsVz1VCLz69Wrl+pRJo2HROQe8qD3zDPxqlFe2q1dlVGQwdey1LqIjh7k9J6lza7ByISK33//vWqDIWvgPSNyH5nlXNpF3D1PoAQ5WQRSllJxVvap2QHm979/nBMqWowxEaY8ybDHH5FrSFuIpKcuXLiA1NRUU/ztGWXBiBHPOuWBs1kpMqleSVc4BhdrkZ4pISGhquGPiJxPgsuUKVNMFVyElAXyoOms9aOaFWCkiiXd6ch6hg4dgp07d+pbRORMWVlZ6quZgotBzkfOS4KMo9eQalaKTNJjK1euctsgHrKfMQlmRcUpfQ8ROYMU2gUFBaYMLraMdFlKyjyHdTqwuwYjY18kPcbgYk0yjYRML8H5yYicR/6+lizJxKxZs0wdXISU5dKeLg3/juplaneAOXTokBppStYVGRmJgwcP6ltE5EjS7pKY+ArS09+2zIO4tKdLr7I333xT39M8dgeYwsJCjga3uH79+iE3N1ffIiJHknYXGdDYs2dPfY81GF2WjYUjm8PuNhh/fz+UlpaZvtpHDeN9JHI8Y/qs9etzTDGrcVMZ59/coQx21WDkzSV/z0LJ+kaNeg5fffWVvkVEjrBs2TKVarJicBGSKpOxMUbvN3vZFWCk/SUsLEzfIiuTqSpkim8icgxpIJfpmKw+fdbw4cORkjJXtSXZy64A880332gRrpu+RVYmixNJexoROYa0a44bN97yGR6pfU2c+IoKlvayK8B8/fXX6Nw5QN8iK+vQoYOazZWImk+e9mWesZiYGH2PtUVHRyMzc4m+1XR2BRiZPdnPz0/fIiuTXOvNlmAloqaT6ZdkGiartr1cT3rAVVVV2j0upskBxsjHsYHfczz8cH+HDawiaslkYKVMw+RJpLF/7969+lbTNDnAnDp1SvU8Is/RrVs3tZ43ETVPfn4+evQI0bc8g9Ri7G2ntStFRp7l7rvvxrlz5/QtIrKHzO8n6WZPmz6re/fuqlnEHk0OMCdPlqsCiTxHcHAwzp49q28RkT3Onz/vkdkdaU/q0iVQBdCmanKAqam5rAokIiKqJ+MDH3jgAX3Ls0RGPqoCaFMxRUZE5CD33nuv/p1nsTeNzgBDREQNsjeNzgBDROQApaWl6NKli75FosmzKRtTOBtTOpP1yT1dtWoV9uwp0PcQUVMFBnZFcnKKRy5jYm+5zwBDvKdEDuDJf0f2fjamyIiIqEGS/uvYsaO+1XgMMEREDlJTU6N/51kuXbqkJsZtqiYHmDZtWqvp+omIqF5oaChKSkr0Lc8iU/a3atVK32q8JgcYmaZfpusnz2Fv9ZeI6vn4+DRr7RSzkhH8J04ct2sKHKbIyO7qLxHVM6bo97SZyaVCYe8UOE0OMLIOjL0Tn5E5yYJj9lR/iehaMTGxOHzYs9Jku3fvRkREhL7VNE0OMMY6MM1Zp5nMxRNngCVyh8ceewzZ2ev0Lc8gSxD07dtX32oau1JksbFPq3VhyPqkOi8LjhFR8/Xq1QsbNnxs18zDZiQLqAl7H0DtCjABAQFq2n6yvpMnT6oFx4io+STDk5Q0Ezt27ND3WJukx0aOHKlvNZ1dAUYmPisrO6pvkZUdP37c7vwqEd1owIABSEtLtXwzgtTCUlLm4vHHH9f3NJ1dAUb6ex84cEDfIiuTfvtunaCvMgdj/f0QnlaEn/RdLY4zrkFNGbalLcLHlXLEn7S3eBn+/oOQVmSSgYAefN+DgoLU+imbNm3S91jTmjVrVG3M6B1nD7sCjPQkkzwjG/qtT3oEeuoiSS2XFlC2voUxaUfws9q+DZ3iF6GiYhMm926j9rhdp3gsrTiF4sm9tbPzPGPGjLF0LUbaZqX2Mnz4cH2PfewKMJJnlIb+r776St9DVlRWVqYa+JvzhEJEN5JajHRZzsrK0vdYS0ZGBtLTFzW7bLArwIjIyEgcPHhQ3yIrkiVeo6Ki9C2zqEbZ9izMjA6Gv7+f9i8CY9NyUFT5o/7zr5EzNgz+CanI+WAmotVrtH/RryGnrFp/jUaliF5ED/XzYETPXIS0sRHwD09F0S1zMj+isuhDm/eW3/uw/r21Y27PsnnPHi8iLacIlbV1P65L+4QhIW01Ppj5tM0xclBWY7yoVjvMlrpzUT9/GjNX7UF9n8xbpLNuSCnd6ly/Q1FaLCISZfbbHCRGBGi/8zm+vnrMalRvf027Ln9GVtkP6kh1fkBZ1p+1z/QatlfLuV5/fLkPW2w+h60a7T0H2fyu+BbbZz567b7aUmTFBaPHzO2ovubz6Pc0OgFjjfeLy0KZ9mu1lXttrqUfeoxNxzbb+2xi48aNw+rVq672xLKKrVu3qLFxgwYN0vfYz+4A069fP+Tm5upbZEWSIzbX2hU/4kzObMQ99w6qRqxDScUplBem4L5N0xCf8C6KbAu3T/+Od4/0xdslFdpr3kcC1iAxbkFdYVZbgZypf8aYTfcjZVsJKsrzMf3Xm5C2+Yz+yzejFfxF7yIh/g3si3gHheUVKNkyC37rtPcevxJlP9Ud87n55zFii3bMiuMoXNwFmxKfRcJbe7Ui1vAdPk37EEf6LtDOX3vN8tHABy8jLmWHFjq1dzmTi6lxL2OT7wxsU+c+Cb/elIOmDc1r6FxzcderG1CYLtOqxyO9sBzFk/vgP+p+UeMF795PYkjrL7Cu4KR2JF3tSRSs+wKthzyJ3t5ayFDHfwtVMcu04xv3QfscU3NxxuY21GmFbr36ofXlT7GlSO+eq12v/RvKAZt9tcf2YF3xHYjs2xXaW9xI5vGS+17+BXLfiEbXK3vxVsIoJFfFIrvwuHYfC7H4vi0YEzcbOWeMBw7zkqf/lJR5SEx8xTKpMkmNvfCCpPfSro55bA67A4xUAauqKj1uWoSWQnqISDvab3/7W32PCVTvRkZSNhAzA288FwppLfDqFIX/Sp6IkJIMvP5RWX2B2Ho4pk+LQ1AbL+01kRg94iGtMPsc+49e0QqyT/Fe3u0YPT0R8UFaUeZ1H56Y+leMbq3/7k19hy+y16JEjjs1Cp28vNAmeDSWHj6Fitzn4LtrKZLytFNLmYHngqV4vB2dnngZyZNDUJK2EB/Z1AZaj/4rpsUHa+evvebxP2FEeGtc3lCEoz/9gGOb/wd5sD33KEydPhwNntoNGjrXBAT90l+19+8wcEgHFK/bg2P6Ba0r/DtgyMDfwbu2DB+9noGS8Jcw7eX+2vHr7oOcJ/IWIGPHt3W/dJURtM7hYPl5dY9qTxxAvoorxj4tKJ4+jjI8iEdDbzUtUQQGazWYNl6dEB7eFsc+Woi0kocwbVoC+na6vf4+IhtJGbtVwDY7eYAbMeJZTJkyxfRBRs5v5Mhn8d57yxw28NruACPkwu3du1ffIispKtqHiRNfcchTiqPUVpXj4OXWCHq4hyrU6miFZ7cw9Gl9GWVl39TXFO5oC+9Wxotuw11t2+nfa4V4wRYUIxx9u7fV92lUoRqgb9yE8cQdFIj7tYL/Wj+iqvwYLiMID4d2tPmj8dae3B/UgsNJlJ2ur8PccY+39kyv82qFth3v0DfO4dCug0Bkb3T3No6iFc7deyNS32qUBs+1Mdqj98An0br4f/FJ8UVtW79mrZ/EwN7tgbOHsav4MtpHhaHL1cMb51mODfsrbuz55d0VfSPv0IOWfrzwcZj8rBbIdh3GWS0oFm35FJfDByKy6536L12nfSD87zGa/PVr1b4PwrrYvF69T3s9YOv7TG7ChAnqa3p6uvpqRhJcJAhKmT5gwEB9b/PZ83/nVRKdV65cqW+Rlch0FjKthZnUfv8dKnAHOrZtde3/mK28cY9WRl+uuogr+q5b+wnfX7j+CVvcCe97GlFP6NgWd93wV2Ecsx3a3mXb58lLO7W22hlXo+piI55OfzqHE1/cZIT3Pf4Itact9abn2hhGjWMvMrOLUX1NesxLuw8XtYCg1ZPS4hCot32ofxEvY3PdAW6iA0IffRAoO47TNdU4XVaJ8CH/iZgenYGCIhz5+ktsWXdO2/cIujbmnGuv4OLZf2snkYr4QJtz8H8EiZutN0o+NTUV5eXlWLx4sb7HPIzgEhYWdjUYOkqzAkzPnj2ZJrMgIz0m01qYiddd7eGPf+PsxSv1qTBxpRrfamVNa9+29TWDW9JqM+3u0b5ewMXvbR9xf0D1t5f17xvwxXGcueHJ+FbHrNVO7aJ2xt7wbduImuBtHdDlIakhXMT3th/w2wocsqfMvOm5NpJeo7u87lPs3berPj2m/cjrrrboqNXLwt/YhvKKU6i47t/Nuxbfia6RAxEubS5bt2jB5DZEhXVDkNp3DMf3HdZqpwHavvsbV+gYNb/wN7Gt/MZzqCiegt4W6t8smQIJMjJ+UApxs6TLpCxwVnARzQowQqpUbOy3lry8PDWAykzpMeHlG4AHJRX22eH6nlmSuz96APskdRZ0r2qXaZhe0F2XtkLNCezfd07fuInb/NErNgD490VUX7kmvGluh29AV63ILcNnh87aBL9qHN1/EJfRGUH3N2Z8ie1TvnGUWlQfKUKBvnVz172mwXNtLD1NdvlzrPr72vr0mOjYA4+G45o2GlFbloU4/2DEZZXaXIN6dffvHD7PfA/r0A+9umk1UbXvn3g9cZ72HnX7Gke/VsVbUHDMpreb3hPN6GVmJUaQkam2nn/+ebc/mMswhWeeiXdacBHNDjBxcXGqK57ZG7Co3pIlmWo6C9Px7o+JKUO1CJiM15YfUu0ttZX5+NuMDJSETMTrfwxq1P+wXl2fxAsxP+KDeel1XZdrz2D7395AWklDNZj2eGjoMIRcXoN5C/LrAlzNIWRJd+Ier6MofAxSYrRTS0rG8lJpXv4RldsXYUZaCUImT8Ifg27RrnANLfj94U+IwXuYMOVDlGpBRj7fgnlrtCBluA0dQx/SAuQhZL6zXn/NZ8hasdHmNQ2dq21X4TKcOHMWx8rO6gMubRlpskPYvPnQ1fRY3Y+64A8vRKN18TuYv2i3On5t5W4smv8Oihu6D3rnga9KSgHjeHqbibjmPX6Rfq204DR/fhb2Slfx2krsXfQ3zC8OweTX43+5M4MJSZCZNm2amt/rkUf6qS7BriZl9YoVKzB27Iuql5uzgoto9i2S3gYyLYInruTmiWTyOl/fTqoXoPncjvvi5yB3+UvwXT0EIf5+CIhIwplB85GT9Rf0bmyDtpc/4hd8iGWDTiPpqRD4B0Rh3s+RGB3SUBuMF9r0/guycl5Dn8KXEBHgB/+QIVjt+xKW507FE227qGMun+aD1QO1Y/oHImLCCQxKX4WsV/s2omZVx+u+OCzIXYbxeBsDQ/y1z7cQPw+KR4j+c+EVNBKZ2bMQWZBU95qof+Dn/gNtXvML5+p9Ozo+PBJT/3ABafERGJxVF6xvcLXjQ8DV9FgduQ//jfycV+GbN0YdPyBiDPJ8X/2F+6DXirT/6mubek3khvf4ZV73xeOd/PWY4bsBQyMCtfv4EIbmdcKMnMV4tbdNBw4Lio+Px549nyMzc4kq4KU24QoyJkdqTzJF1Pr1OU4fpvCr/9Po39tNCq2FCxdi7dq1+h4yq2HDhmHSpEkmG//iCjKYLxaJeAOFS+PRSd9L5G45OTlqWhl5UJcpZpzx8Cdl9CeffKIGULry798hlUzjZOVDkHkZ98ezg0utPlI9AmOvPrlXoyxnCd7dfCdiBvdGR7WPyBykNrNx4yY1q7mkreQhUFJnzV1TRtp4JBUmx5MKwODBg1UlwJV//w6pwQjWYsyvxdReaitRlLsS7ySlYrPRcBHyPN6YnoA/PhHU6HQWkTtIWbpz505kZLyt5nyUabkCAwPRoUOHW9ZupF1FFoGUdbpkKRVZhVJ6+EonLPl7lx6/7uCwACNabvrF/PgAQGQ90jYjcwYWFhbiwoULanjBrUgwkh5qsl6XLKlihnZWhwYYaUCSeXekume2LrAtHYM/EbmaQzv6STXMExba8TTSiOjj48PgQkQu5dAajJCGJenfLV3wHDVhGtlPGgplMNXSpf8waddkIvJUDq3BCAkqycnz1II15H4LFixQDX0MLkTkag4PMGLo0KGqv7U7RqlSPbn+MgA2ISFB30NE5DoOT5EZpPeD9OleuXIVU2VuYKTG0tPfdlsXRSJq2ZwWYIQ0LkuDv0zwxl5lriXTT0j/+VGjRul7iIhcyykpMoOMUBVZWVnqK7mGjN4VkqokInIXpwYYMXfuXDXbMqeRcQ25zjJb8qxZs1hrJCK3cmqKzCDtMU89FYVt2/LZm8mJpIu4rKnNdhciMgOn12CEBJXVq9eqRn+ufukcRnCZPXs2gwsRmYJLAoyQUeTjxo1XhWBzZwmla8lEd2+++aYa7zJgwEB9LxGRe7kkRWZr8eLFal1q9ixzDAkuzlxTm4jIXi6rwRikEJTCUApFLrPcPAwuRGRmLg8wwjbIsE3GPgwuRGR2bgkwwggy0ibDINM0cr1kXW0GFyIyM7cFGCGFo/R6kiAja8nQL5Mu33K94uLiGFyIyNRc3sh/MzI4MClpOiZPnnJ19D/dSCavfOGFMarLN9d2ISKzM0WAEZL2mTx5Mvr06YPExET2MLMh7S3p6enIy9vAyUOJyDLcmiKzJYXm+++/r76Pjh6kUkFUlxKT9pZLly6ppagZXIjIKkxTg7ElqaA5c+aogZkyYWNLrM1IrSU7OxszZkzHe+8t4wBKIrIc09RgbElhun59DkpKStTTe0vrAGDUWgoKCtTS0wwuRGRFpqzB2DI6AERGPoqpU6eiffv2+k88j0yhs2TJEtXWIr3rGFiIyMpMWYOxJb2lpO0hJCQE4eFhaqoZT5vLTNJh8rnk83l7e6vPy+BCRFZn+gAjpA1GVmYsLj6gtj0l0Mj5y+eQTg1CPp+MbWEPOiLyBJYIMAZJj0kBbBto5s+fb7keZ3K+Ro1FSHuTfC5PTv8RUctj+jaYhkgNYMeOHUhLS4WvbyeMHz8OvXv3MWVBLedaVLQPmZlLUFVVqXrIxcTEMKgQkceydICxJT3NNm7ciIyMtxEb+zSGDh2CHj1C3DpuxAgq2dnrsGHDx5g48RU89thjHIVPRC2CxwQYgzSY79+/Hzt37lS9saRmExUVpVZ57Ny5s1MDjgSUI0eOqGCXn5+vaioxMbEqqPTq1YttK0TUonhcgLmetHccOnQIhYWFKCjYhRMnjmPUqOdUr7Q2bdogNDRUvc7Pz69RAUAC2KlTp9T3ctyamho1XkeOLaQ7dUREhDquLBVNRNRSeXyAuZ7UMs6fP39NcLhw4YJKYdnq0iVQBQsjKNmSFFy7du3wwAMP4N5779Ve20V9z/YUIqJ6LS7ANJYRiHx8fBg4iIjswABDREROYalxMEREZB0MMERE5BQMMERE5BQMMERE5BQMMERE5BQMMERE5BQMMERE5ATA/wNO+T0akSC8xAAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the charge on the surface of the sphere is +18 μC.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe, in terms of electron flow, how the smaller sphere becomes charged.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Predict the charge on each sphere.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mi>V</mi><mi>R</mi></mrow><mi>k</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>48</mn></mrow><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mn>18</mn><mo>.</mo><mn>2</mn></math> «μC» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electrons leave the small sphere «making it positively charged» ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mfrac><msub><mi>q</mi><mn>1</mn></msub><mn>48</mn></mfrac><mo>=</mo><mi>k</mi><mfrac><msub><mi>q</mi><mn>2</mn></msub><mn>24</mn></mfrac><mo>⇒</mo><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>2</mn><msub><mi>q</mi><mn>2</mn></msub></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>1</mn></msub><mo>+</mo><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>18</mn></math> ✓</p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><mn>12</mn></math> «μC», <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>q</mi><mn>2</mn></msub><mo>=</mo><mn>6</mn><mo>.</mo><mn>0</mn></math> «μC» ✓</p>
<p> </p>
<p><em>Award <strong>[3]</strong> marks for a bald correct answer.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two identical positive point charges X and Y are placed 0.30 m apart on a horizontal line. O is the point midway between X and Y. The charge on X and the charge on Y is +4.0 µC.</p>
</div>
<div class="specification">
<p>A positive charge Z is released from rest 0.010 m from O on the line between X and Y. Z then begins to oscillate about point O.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAT4AAAAsCAYAAAD8UdQUAAAE2klEQVR4nO3cX0hbZxgG8KdeeCEiQgctHZqIgtVVKfGm86Z1K6ItdVZYYbCxFnXVbtQ6kdVFbWeKdB01/tvo0KKjY7szurEOxTYZlF205DA2C7ZrN21JTMGiRhEqM+9u1LotaVNnzol+zw9ycyKel5zvPOc933eSLSIiICJSSIzRBRAR6Y3BR0TKYfARkXIYfESkHAYfESnH0OBLM6cYufuwbIQaNyp+thSMHuOCHR8RKYfBR0TKYfARkXIYfESkHAYfESmHwUdEymHwEZFyGHxEpJwt4fwsFR80JaLN4N7YnwDCDL5ISTOnrBQSrTZCjRsVP1sKRo9xwVtdIlIOg4+IlMPgIyLlMPiISDkMPiJSDoOPiJTD4CMi5TD4iEg5hj7ATERkBHZ8RKQcnYIvgDmtAwfNr+K93tuY+8/7ftzprUR2ZjUGvAv6lBRUAH7XGWSbU5AW8rUXDa5JA2sk2iyWc+EVHLTfCpILADAJV/1epK13NohupsTdUiKpphKxu6dWbV+UWXe7HDDtkUrHuCzqV9CLmR2R3tI9klrQLu7ZqK0yys3IXadDeq1FkmoyL72KpL7nB3FPPDG6ODJEqFwQiWQ26Bh8IjJ7U+wFmf8Ij0WPQyozMuVAy02Z1bWYF7F0cDIqpHd0xuhiNqZFjzgbiyQ1o0zsw3dXjvXihFv6W8oky1QkZ5ye6L3wUeQEyYXV27MqHOJZ54Ghb/DJv4JucVz6K6K9i3oiHscpyYr2jjSqLV84Tkm/J1hn97z3aXNb7uxWN0BLYyJC2aB78D0NkkIpLy2M+sG+EtSNwzLB1FubGafUZ2RKcc9o6AvHjFPqM8ySZXUKe2oVrb7lfbwUhMFuf9eHAau6sdhRVA1b4RSuD08hv7kah3bE6l9GOOZuob3UiiFTBWy1edjONfA1CMCvOTEw/xJ2mbeGXk1L2IXXS5Ix3+eE5g/oWSBFhURYquy4WOhFp7UGH1p7gKrTKLMkRmRvhpzKAZ+GwZ98AHy4MajBF5XjfBpa13l0jufj4uXjsMQz9dZmAY/G7mMeSUh7Of75fz5/H+OPjFzZJ8PEJONQw0fIH3fhOo7BVp6DMEbM2nYVof8b2txtXGn8FEOmk+juPYmkH60obwu1lG2UBXj7P8HRNm90d6REm0xMfCK2AojLyUJaBJsNnYNvGlpXI2w/70ZDayn27TsGW9VO3Gk7j25tWt9SniHgvYpzHw8hqaodF4qT+ZT3/xKLbeZUxOEh7nnCuLzFpcK0jRcaiiwdz+kF+Fyfo6HNi/zmOryTngAgEZby0/ggYxSd1ivQ5qLgnndpXu9Gbh1aIthqqyMGCZY8vBE3iZGxxwh5hP0juNb3AHElebAk8FJDkaXbCAt4r6LpxDfAu+fQWLSqi4rPQVlrHV4bv4SGz5wGz/c9ndezNR1BOuf11kfCbhwu34nfLlzC90Gfvp+GdrkD36IYthO5SNC9QFKNPmf2M1dHYxCffgRnm/Px8Kt6NH33IHRXEGn+X+Do0oD5ftTkpof82lp2vQt+o2rckBJhqepA95t/oGb/+2i99vvKnG7Ap2HAXoujbX/h7S9qOZ9KuuCvs5COFuDThjHY9yVsX/+6tC0bb509jsMF+2HZztAjfTD4iEg5nMQiIuUw+IhIOQw+IlLO32yMdHkK1HwLAAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the electric potential at O.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, the variation of the electric potential <em>V</em> with distance between X and Y.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the direction of the resultant force acting on Z as it oscillates.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the motion of Z is simple harmonic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>k</mi><mi>Q</mi></mrow><mi>r</mi></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mfenced><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>15</mn></mrow></mfrac></math> <em><strong>OR</strong> </em>240 «kV» for one charge calculated ✓</p>
<p>480 «kV» for both ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be seen or implied from calculation.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong> for <strong>MP3</strong>.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>symmetric curve around 0 with potential always positive, “bowl shape up” and curve not touching the horizontal axis. ✓</p>
<p>clear asymptotes at X and Y ✓</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force is towards O ✓</p>
<p>always ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>motion is not SHM ✓</p>
<p>«because SHM requires force proportional to r and» this force depends on <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>motion is not SHM ✓</p>
<p>energy-distance «graph must be parabolic for SHM and this» graph is not parabolic ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well approached. Two common errors were either starting with the wrong equation (electric potential energy or Coulomb's law) or subtracting the potentials rather than adding them.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates drew a graph that was awarded two marks. Many had a generally correct shape, but common errors were drawing the graph touching the x-axis at O and drawing a general parabola with no clear asymptotes.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates were able to identify the direction of the force on the particle at position Z, but a common error was to miss that the question was about the direction as the particle was oscillating. Examiners were looking for a clear understanding that the force was always directed toward the equilibrium position, and not just at the moment shown in the diagram.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a challenging question for candidates. Most simply assumed that because the charge was oscillating that this meant the motion was simple harmonic. Some did recognize that it was not, and most of those candidates correctly identified that the relationship between force and displacement was an inverse square.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br>