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title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <p><img alt="" src="../../electricity/phone.jpg" style="float: left; width: 250px; height: 167px;">In an electrical circuit, electrons move due to potential difference. Electric fields caused by charged plates, point charges or charged spheres cause lone charges to accelerate. This changes their energy.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div>Uniform fields</div> <div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field lines</p> </div> </div> <div class="panel-body"> <div> <p>A uniform field has a constant field strength. Field lines are equidistant and parallel, and show the direction of force acting on a positive test charge. Uniform electric fields are formed between oppositely charged parallel plates.</p> <p style="text-align: center;"><img alt="" src="../../fields/uniform-electric.png" style="width: 300px; height: 213px;"></p> <p>Beyond the edges of the plates, the field would no longer be uniform, but these are not drawn.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field strength</p> </div> </div> <div class="panel-body"> <div> <p>Electric field strength is defined as the force per unit charge:</p> <p style="text-align: center;"><span class="math-tex">\(E={F_e\over q}\)</span></p> <p>Field strength is equal to the magnitude of the potential gradient:</p> <p style="text-align: center;"><span class="math-tex">\(E={V_e\over d}\)</span></p> <p>These equations are often combined, for example to find the force acting on a given charge:</p> <p style="text-align: center;"><span class="math-tex">\({F_e\over q}={V_e\over d}\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is electric field strength (NC<sup>-1</sup> or Vm<sup>-1</sup>)</li> <li><span class="math-tex">\(F_e\)</span> is electric force (N)</li> <li><span class="math-tex">\(q\)</span> is the charge placed in the field (C)</li> <li><span class="math-tex">\(V_e\)</span> is the potential difference between the plates (V)</li> <li><span class="math-tex">\(d\)</span> is the distance between the plates (m)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Calculating energy changes</p> </div> </div> <div class="panel-body"> <div> <p>The energy changes that take place in electric fields are between electric potential energy and kinetic energy:</p> <ul> <li>Work can be done by a charge on the field if it moves towards the plate of like charge; the charge loses kinetic energy and gains potential energy.</li> <li>Work is done by the field on the charge if it is attracted to the plate of opposite charge; the charge loses potential energy and gains kinetic energy.</li> </ul> <p>Since electric field strength is constant, the force acting on the charge is constant everywhere. Work is done when a charge moves along a field line, perpendicular to the plates:</p> <p style="text-align: center;"><span class="math-tex">\(W=F_{e}s=\Delta E_p=q\Delta V_e\)</span></p> <ul> <li><span class="math-tex">\(W\)</span> is work done (J)</li> <li><span class="math-tex">\(F_e\)</span> is electric force (N)</li> <li><span class="math-tex">\(s\)</span> is displacement parallel to field lines (m)</li> <li><span class="math-tex">\(\Delta E_p\)</span> is change in potential energy (J)</li> <li><span class="math-tex">\(q\)</span> is charge (C)</li> <li><span class="math-tex">\(\Delta V_e\)</span> is potential difference</li> </ul> <p>No work is done parallel to the plates. This is because the charge would be moving along an equipotential surface.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Equipotential surfaces</p> </div> </div> <div class="panel-body"> <div> <p>Equipotential surfaces are planes of constant potential. They are always perpendicular to the field lines. For a uniform field, equipotentials are equidistant and parallel, here shown in red:</p> <p style="text-align: center;"><img alt="" src="../../fields/uniform-equi.png" style="width: 291px; height: 200px;"></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div>Radial fields</div> <div> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field lines</p> </div> </div> <div class="panel-body"> <div> <p>Radial fields are produced by point charges or charged spheres. Field strength increases with proximity to the charge. This is indicated by closer field lines. The direction of the field lines shows the direction of force acting on a positive test charge placed in the field.</p> <p style="text-align: center;"><img alt="" src="../../fields/radial-electric.png" style="width: 137px; height: 145px;"></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field strength</p> </div> </div> <div class="panel-body"> <div> <p>As radial fields are non-unifom, electric force and field strength are not constant. Electric force is found using Coulomb's law:</p> <p style="text-align: center;"><span class="math-tex">\(F_e=k{Qq\over r^2}\)</span></p> <p>Electric field strength is the force per unit charge:</p> <p style="text-align: center;"><span class="math-tex">\(E={F_e\over q}=k{Q\over r^2}\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is electric field strength (NC<sup>-1</sup>)</li> <li><span class="math-tex">\(F_e\)</span> is electric force (N)</li> <li><span class="math-tex">\(q\)</span> is the charge placed in the field (C)</li> <li><span class="math-tex">\(k\)</span> is a constant (8.99×10<sup>9</sup> N m<sup>2</sup> C<sup>−2</sup>)</li> <li><span class="math-tex">\(Q\)</span> is the charge producing the field (C)</li> <li><span class="math-tex">\(r\)</span> is the distance between the centres of the charges (m)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Calculating energy changes</p> </div> </div> <div class="panel-body"> <div> <p>Electric potential is the work done per unit charge in bringing a positive test charge from infinity to a point in an electric field at a small constant speed.</p> <p>As force is not constant, electric potential is found by integrating the force with respect to distance from infinity:</p> <p style="text-align: center;"><span class="math-tex">\(V_e={\int_\infty^r F_e\,\mathrm{d}r\over q}= {\int_\infty^r {kQq\over r^2}\,\mathrm{d}r\over q}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow V_e=k{Q\over r}\)</span></p> <ul> <li><span class="math-tex">\(V_e\)</span> is electric potential (JC<sup>-1</sup> or V)</li> <li><span class="math-tex">\(k\)</span> is a constant (8.99×10<sup>9</sup> N m<sup>2</sup> C<sup>−2</sup>)</li> <li><span class="math-tex">\(Q\)</span> is the charge producing the field (C)</li> <li><span class="math-tex">\(r\)</span> is the distance between the centres of the charges (m)</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/173041346"></iframe></div> <p>As with energy and work done, potential is a scalar quantity.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/173788234"></iframe></div> </div> <p> </p> <p>Energy is changed when an object is moved through a distance by a force. When a charge is moved into or out of a non-uniform electric field, it will be attracted or repelled. Therefore, work is done and energy becomes stored in the charge itself. This energy is electrical potential energy and is measured in J.</p> <p style="text-align: center;"><span class="math-tex">\(E_p=qV_e=k{Qq\over r}\)</span></p> <p> </p> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Equipotential surfaces</p> </div> </div> <div class="panel-body"> <div> <p>The equipotential surfaces in a radial field are spherical, shown as circles on a 2-dimensional diagram. As potential varies with <span class="math-tex">\(1\over r\)</span> from the centre of the charge, the equipotentials increase in spacing outward from the centre.</p> <p style="text-align: center;"><img alt="" src="../../fields/radial-equi.png" style="width: 137px; height: 145px;"></p> <p>Work is done when a charge is moved between equipotentials:</p> <p style="text-align: center;"><span class="math-tex">\(W=q\Delta V_e=q\times kQ({1\over r_f}-{1\over r_i})\)</span></p> <ul> <li><span class="math-tex">\(W\)</span> is work done (J)</li> <li><span class="math-tex">\(q\)</span> is the moving charge (C)</li> <li><span class="math-tex">\(\Delta V_e\)</span> is electric potential difference (JC<sup>-1</sup> or V)</li> <li><span class="math-tex">\(k\)</span> is a constant (8.99×10<sup>9</sup> N m<sup>2</sup> C<sup>−2</sup>)</li> <li><span class="math-tex">\(Q\)</span> is the charge producing the field (C)</li> <li><span class="math-tex">\(r\)</span> is the initial or final distance between the centres of the charges (m)</li> </ul> <p>Potential gradient is the ratio of the difference in potential to the distance between the equipotential surfaces. Its magnitude is equal to electric field strength:</p> <p style="text-align: center;"><span class="math-tex">\(E=-{\Delta V_e\over \Delta r}\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is electric field strength (NC<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta V_e\)</span> is potential difference (JC<sup>-1</sup> or V)</li> <li><span class="math-tex">\(\Delta r\)</span> is the distance between the potentials (m)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Inside a charged sphere</p> </div> </div> <div class="panel-body"> <div> <p>So far we have examined only the electric field outside of the charge producing the field. What about the field strengths and potentials at radii less than the radius of the sphere?</p> <ol> <li>A sphere may have uniform distribution of charge:</li> </ol> <p style="text-align: center;"><img alt="" src="../../fields/gaussian-sphere.png" style="width: 400px; height: 233px;"></p> <h6 style="text-align: center;">By Ag2gaeh - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49540033</h6> <p>The charge enclosed within the sphere by a radius <span class="math-tex">\(r\)</span> in comparison with the total radius <span class="math-tex">\(R\)</span> is related to the volume:</p> <p style="text-align: center;"><span class="math-tex">\({q\over Q}={r^3\over R^3}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(E=k{q\over r^2}=k{Qr\over R^3}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(V_e=k{q\over r}=k{Qr^2\over R^3}\)</span></p> <ol start="2"> <li>The sphere may alternatively be a conductor. In this case the charge would move to the surface. In this situation, the field at any radius within the sphere would be zero; the potential would be the same as at the surface.</li> </ol> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <p><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="Normal" data-topics="1029,537" data-subject-id="6" data-n-flashcards="10" style="text-align:center">Show flashcards</a></div><hr> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#e6247095"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="e6247095"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Electric potential <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-96-353" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A small test charge is close to a sphere of charge.</p><p style="text-align: center;"><img alt="" src="../../epotq1.jpg" style="width: 439px; height: 191px;"></p><p>If point P is at zero potential the potential energy the electrical PE of the test charge is not equal to</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> the loss of PE as the test charge is released and reaches P</label></p><p><label class="radio"><input type="radio"> the KE gained when the charge is released and reaches P</label></p><p><label class="radio"><input type="radio"> the work done in moving the charge from P to this position</label></p><p><label class="radio"><input class="c" type="radio"> Fx</label></p></div><div class="q-explanation"><p>The force is not constant so work done will not equal Fx</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following lines gives the correct relationship between electric potential of a point charge and distance from it.</p><p style="text-align: center;"><img alt="" src="../../epotq2.jpg" style="width: 275px; height: 267px;"></p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>V is proportional to 1/r</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A small test charge q is moved from infinity to a point close to a sphere of charge Q and the force measured</p><p>The potential can be found from:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> the area under the force vs displacement graph divided by q</label></p><p><label class="radio"><input type="radio"> the area under the force displacement graph divided by Q</label></p><p><label class="radio"><input type="radio"> the area under the force time graph divided by the q</label></p><p><label class="radio"><input type="radio"> the area under the force displacement graph</label></p></div><div class="q-explanation"><p>Work done for a small step = Fx</p><p>Potential = work done/q</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The graph below shows the line of y = 1/x</p><p style="text-align: center;"><img alt="" src="../../epotq4.jpg" style="width: 270px; height: 237px;"></p><p>The area of the shaded part is:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 0.75</label></p><p><label class="radio"><input type="radio"> 0.25</label></p><p><label class="radio"><input type="radio"> 0.50</label></p><p><label class="radio"><input type="radio"> 1.00</label></p></div><div class="q-explanation"><p>Area of a trapezium = 1/2(y<sub>1</sub> +y<sub>2</sub>)Δx</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The small test charge moves from right to left between the two charges shown.</p><p style="text-align: center;"><img alt="" src="../../epotq5.jpg" style="width: 563px; height: 400px;"></p><p>Which graph represents the force experienced by the test charge vs distance from the left hand charge?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>Force is to the left (-) when furthest to the right and to the right (+) when close to the charge on the left</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents a 2C test charge so far from a sphere of charge that there is no force experienced by it.</p><p style="text-align: center;"><img alt="" src="../../epotq6.jpg" style="width: 351px; height: 58px;"></p><p>The amount of work done moving to P is 10 J. The potential at P is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 10 V</label></p><p><label class="radio"><input type="radio"> 20 V</label></p><p><label class="radio"><input type="radio"> 0.2 V</label></p><p><label class="radio"><input class="c" type="radio"> 5 V</label></p></div><div class="q-explanation"><p>Potential is work done per unit charge</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The graph represents the force applied to a 2C test charge as it is moved in an electric field.</p><p style="text-align: center;"><img alt="" src="../../epotq7.jpg" style="width: 319px; height: 256px;"></p><p>The change in potential is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 32 V</label></p><p><label class="radio"><input type="radio"> 2 V</label></p><p><label class="radio"><input type="radio"> 16 V</label></p><p><label class="radio"><input class="c" type="radio"> 8 V</label></p></div><div class="q-explanation"><p>Work done = area = 1/2 x 8 x 4 = 16 J</p><p>Potential = work done/charge</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents the path of a 2 C test charge moving between A and B via a path that passes through points C and D. The potential at these points is shown.</p><p style="text-align: center;"><img alt="" src="../../epotq8.jpg" style="width: 537px; height: 198px;"></p><p>The work done is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 2 J</label></p><p><label class="radio"><input type="radio"> 17 J</label></p><p><label class="radio"><input type="radio"> 34 J</label></p><p><label class="radio"><input class="c" type="radio"> 4 J</label></p></div><div class="q-explanation"><p>The work done is independent of path- Work done = potential difference x charge</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents a charge with two lines of equipotential, one at 10 V the other at 20 V.</p><p style="text-align: center;"><img alt="" src="../../epotq9.jpg" style="width: 244px; height: 227px;"></p><p>The work done moving the 2 C test charge from A to B is</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 0 J</label></p><p><label class="radio"><input type="radio"> 40 J</label></p><p><label class="radio"><input type="radio"> 10 J</label></p><p><label class="radio"><input type="radio"> 20 J</label></p></div><div class="q-explanation"><p>The potential at B is the same as A as it is on the same line of equipotential</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents a charge with two lines of equipotential, one at 10 V the other at 20 V.</p><p style="text-align: center;"><img alt="" src="../../epotq9.jpg" style="width: 244px; height: 227px;"></p><p>The work done moving the 2 C test charge from A to C is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 10 J</label></p><p><label class="radio"><input type="radio"> 40 J</label></p><p><label class="radio"><input type="radio"> 0 J</label></p><p><label class="radio"><input class="c" type="radio"> 20 J</label></p></div><div class="q-explanation"><p>The potential difference = 10 V</p><p>Work done = Vq</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The potential at the surface of a charged sphere, so far from the Earth that the force on it is negligible, is 10 V. The potential at the surface of the Earth is 100 V.</p><p style="text-align: center;"><img alt="" src="../../epotq10.jpg" style="width: 563px; height: 245px;"></p><p>If the sphere is moved close to the surface of the Earth the potential at its surface will be</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 110 V</label></p><p><label class="radio"><input type="radio"> 100 V</label></p><p><label class="radio"><input type="radio"> 10 V</label></p><p><label class="radio"><input type="radio"> 90 V</label></p></div><div class="q-explanation"><p>Potential will be higher due to presence of the Earth.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Two spheres so far from the Earth that the electric force is negligible, have potentials shown.</p><p style="text-align: center;"><img alt="" src="../../epotq11.jpg" style="width: 563px; height: 245px;"></p><p>Both charges are moved close to the Earth. The potential difference between the charges will be</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 20 V</label></p><p><label class="radio"><input type="radio"> 200 V</label></p><p><label class="radio"><input class="c" type="radio"> 2 V</label></p><p><label class="radio"><input type="radio"> 0 V</label></p></div><div class="q-explanation"><p>The charges will have potential 110 V and 112 V so pd is 2 V.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram represents 2 charged spheres close to the Earth-</p><p style="text-align: center;"><img alt="" src="../../epotq12.jpg" style="width: 327px; height: 245px;"></p><p>The potential at the Earth´s surface is 100 V and the potential difference between A and B is 2 V.</p><p>What is the potential difference between A and B when the potential of the Earth is raised to 200 V?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 200 V</label></p><p><label class="radio"><input type="radio"> 202 V</label></p><p><label class="radio"><input type="radio"> 102 V</label></p><p><label class="radio"><input class="c" type="radio"> 2 V</label></p></div><div class="q-explanation"><p>The potential of both charges will be raised by 100 V.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam-style Questions</p> </div> </div> <div class="panel-body"> <div> <p><em>Online tutorials to help you solve original problems</em></p> <iframe src="../../../pages/subjects/page-networks/index-58.htm?ticket=082b9c9c4ae3624d&network-id=53&sitename=physics&subject-id=6&fullscreen=false&node=start" style="width: 100%; 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