HL Paper 2
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.
Outline what is meant by electric field strength.
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.
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.
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.
The photons cause the emission of electrons from the photoelectric surface. The work function of the photoelectric surface is 5.1 eV.
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.
Show that the energy of photons from the UV lamp is about 10 eV.
Calculate, in J, the maximum kinetic energy of the emitted electrons.
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.
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.
On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.
An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.
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.
The following data are available for the lamps when at their working temperature.
Lamp specifications 24 V, 5.0 W
Power supply emf 24 V
Power supply maximum current 8.0 A
Length of each rod 12.5 m
Resistivity of rod metal 7.2 × 10–7 Ω m
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.
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.
Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.
One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline one other electrical advantage of this system compared to one in which the lamps are connected in series.
Outline how eddy currents reduce transformer efficiency.
Determine the peak current in the primary coil when operating with the maximum number of lamps.
A beam of electrons e– 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.
The magnetic field is adjusted until the electron beam is undeflected as shown.
Identify, on the diagram, the direction of the electric field between the plates.
The following data are available.
Separation of the plates RS = 4.0 cm Potential difference between the plates = 2.2 kV Velocity of the electrons = 5.0×105 m s–1
Determine the strength of the magnetic field B.
The velocity of the electrons is now increased. Explain the effect that this will have on the path of the electron beam.
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.
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 10–8 Ω m.
output power = 110 MW
To ensure that the power supply cannot be interrupted, two identical cables are connected in parallel.
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.
Calculate the radius of each wire.
Calculate the peak current in the cable.
Determine the power dissipated in the cable per unit length.
Calculate the root mean square (rms) current in each cable.
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).
Suggest the advantage of using a step-up transformer in this way.
The use of alternating current (ac) in a transformer gives rise to energy losses. State how eddy current loss is minimized in the transformer.
The graph shows how current varies with potential difference across a component X.
Component X and a cell of negligible internal resistance are placed in a circuit.
A variable resistor R is connected in series with component X. The ammeter reads .
Component X and the cell are now placed in a potential divider circuit.
Outline why component X is considered non-ohmic.
Determine the resistance of the variable resistor.
Calculate the power dissipated in the circuit.
State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.
Slider S of the potential divider is positioned so that the ammeter reads . Explain, without further calculation, any difference in the power transferred by the potential divider arrangement over the arrangement in (b).
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.
Satellite Y orbits closer to the centre of Earth than satellite X. Outline why
The cable acts as a spring. Satellite Y has a mass m of 3.5 x 102 kg. Under certain circumstances, satellite Y will perform simple harmonic motion (SHM) with a period T of 5.2 s.
Satellite X orbits 6600 km from the centre of the Earth.
Mass of the Earth = 6.0 x 1024 kg
Show that the orbital speed of satellite X is about 8 km s–1.
the orbital times for X and Y are different.
satellite Y requires a propulsion system.
The cable between the satellites cuts the magnetic field lines of the Earth at right angles.
Explain why satellite X becomes positively charged.
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.
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.
Estimate the value of k in the following expression.
T =
Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.
Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.
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.
The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.
Determine the total resistance of the lamps when they are working normally.
Calculate the current in the primary of the transformer assuming that it is ideal.
Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.
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.
Explain why the pendulum comes to rest after a smaller number of swings.
Rhodium-106 () decays into palladium-106 () by beta minus (β–) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the β– decay.
Bohr modified the Rutherford model by introducing the condition mvr = n. Outline the reason for this modification.
Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression
where k is the Coulomb constant.
Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.
Calculate the electron’s orbital radius in (c)(ii).
Explain what may be deduced about the energy of the electron in the β– decay.
Suggest why the β– decay is followed by the emission of a gamma ray photon.
Calculate the wavelength of the gamma ray photon in (d)(ii).
An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.
The following data are available for the conductor:
density of free electrons = 8.5 × 1022 cm−3
resistivity ρ = 1.7 × 10−8 Ωm
dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.
The ammeter reading is 2.0 A.
The electric field E inside the sample can be approximated as the uniform electric field between two parallel plates.
An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.
The following data are available for the conductor:
density of free electrons = 8.5 × 1022 cm−3
resistivity ρ = 1.7 × 10−8 Ωm
dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.
The ammeter reading is 2.0 A.
Calculate the resistance of the conductor.
Calculate the drift speed v of the electrons in the conductor in cm s–1.
Determine the electric field strength E.
Show that .
The diagram shows a potential divider circuit used to measure the emf E of a cell X. Both cells have negligible internal resistance.
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.
State what is meant by the emf of a cell.
Show that the resistance of the wire AC is 28 Ω.
Determine E.
Cell X is replaced by a second cell of identical emf E but with internal resistance 2.0 Ω. Comment on the length of AC for which the current in the second cell is zero.
Two equal positive fixed point charges Q = +44 μC and point P are at the vertices of an equilateral triangle of side 0.48 m.
Point P is now moved closer to the charges.
A point charge q = −2.0 μC and mass 0.25 kg is placed at P. When x is small compared to d, the magnitude of the net force on q is F ≈ 115x.
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.
Show that the magnitude of the resultant electric field at P is 3 MN C−1
State the direction of the resultant electric field at P.
Explain why q will perform simple harmonic oscillations when it is released.
Calculate the period of oscillations of q.
At t = 0, the switch is connected to X. On the axes, draw a sketch graph to show the variation with time of the voltage VR across R.
The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage Vc drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.
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.
The mass of ions ejected each second is 6.6 × 10–6 kg and the speed of each ion is 5.2 × 104 m s–1. 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.
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.
In practice, the ions leave the spacecraft at a range of angles as shown.
Determine the initial acceleration of the spacecraft.
(i) Estimate the maximum speed of the spacecraft.
(ii) Outline why the answer to (i) is an estimate.
Outline why scientists sometimes use estimates in making calculations.
Outline why the ions are likely to spread out.
Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.
A square loop of side 5.0 cm enters a region of uniform magnetic field at t = 0. The loop exits the region of magnetic field at t = 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.
Show that the speed of the loop is 20 cm s−1.
Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage in the loop.
Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.
There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.
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.
Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.
The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg−1 K−1. Estimate the increase in temperature of the wire.
The diagram shows the electric field lines of a positively charged conducting sphere of radius and charge .
Points A and B are located on the same field line.
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 . Point A is at a distance of from the centre of the sphere. Point B is at a distance of from the centre of the sphere.
Explain why the electric potential decreases from A to B.
Draw, on the axes, the variation of electric potential with distance from the centre of the sphere.
Calculate the electric potential difference between points A and B.
Determine the charge of the sphere.
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.
A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.
When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.
Electricity can be generated using renewable resources.
The voltmeter is used in another circuit that contains two secondary cells.
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.
Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.
State the emf of the cell.
Deduce the internal resistance of the cell.
Calculate the reading on the voltmeter.
Comment on the implications of your answer to (c)(i) for cell B.
Outline why electricity is a secondary energy source.
Some fuel sources are renewable. Outline what is meant by renewable.
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.
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−2.
The overall efficiency of the re-charging process is 18 %.
Calculate the minimum time required to re-charge the cell fully.
Outline why research into solar cell technology is important to society.
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.
The speed of the proton is 2.16 × 106 m s-1 and the magnetic field strength is 0.042 T.
Label with arrows on the diagram the magnetic force F on the proton.
Label with arrows on the diagram the velocity vector v of the proton.
For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.
For this proton, calculate, in s, the time for one full revolution.
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.
The centre of the ball, still carrying a charge of 1.2 × 10−6 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 is the point on the line joining the charges where the electric field strength is zero. The distance PQ is 0.22 m.
The charge per unit area on the surface of the wall is σ. It can be shown that the electric field strength E due to the charge on the wall is given by the equation
.
Demonstrate that the units of the quantities in this equation are consistent.
The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.
Determine the horizontal force that acts on the ball.
The charge on the ball is 1.2 × 10−6 C. Determine σ.
The thread breaks. Explain the initial subsequent motion of the ball.
Calculate the charge on Q. State your answer to an appropriate number of significant figures.
Outline, without calculation, whether or not the electric potential at P is zero.
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.
When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.
The switch S is initially open. Calculate the total power dissipated in the circuit.
The switch is now closed. State, without calculation, why the current in the cell will increase.
The switch is now closed. .
The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.
The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.
Calculate the energy stored in the capacitor.
Calculate the change in the energy stored in the capacitor.
Suggest, in terms of conservation of energy, the cause for the above change.
In an experiment a beam of electrons with energy 440 MeV are incident on oxygen-16 nuclei. The variation with scattering angle of the relative intensity of the scattered electrons is shown.
Identify a property of electrons demonstrated by this experiment.
Show that the energy E of each electron in the beam is about 7 × 10−11 J.
The de Broglie wavelength for an electron is given by . Show that the diameter of an oxygen-16 nucleus is about 4 fm.
Estimate, using the result in (a)(iii), the volume of a tin-118 nucleus. State your answer to an appropriate number of significant figures.
A negatively charged thundercloud above the Earth’s surface may be modelled by a parallel plate capacitor.
The lower plate of the capacitor is the Earth’s surface and the upper plate is the base of the thundercloud.
The following data are available.
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.
Show that the capacitance of this arrangement is C = 6.6 × 10–7 F.
Calculate in V, the potential difference between the thundercloud and the Earth’s surface.
Calculate in J, the energy stored in the system.
Show that about –11 C of charge is delivered to the Earth’s surface.
Calculate, in A, the average current during the discharge.
State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.
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.
The following data are available:
Length of cable = 10 m
Cross-sectional area of cable = 6.0 mm2
Resistivity of copper = 1.7 × 10–8 Ω m
Calculate the power dissipated in the cable.
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.
The capacitance of Y is 12 μF. S is now closed.
Calculate, in J, the energy stored in X with the switch S open.
Calculate the final charge on X and the final charge on Y.
Calculate the final total energy, in J, stored in X and Y.
Suggest why the answers to (a) and (b)(ii) are different.
A conducting sphere has radius 48 cm. The electric potential on the surface of the sphere is 3.4 × 105 V.
The sphere is connected by a long conducting wire to a second conducting sphere of radius 24 cm. The second sphere is initially uncharged.
Show that the charge on the surface of the sphere is +18 μC.
Describe, in terms of electron flow, how the smaller sphere becomes charged.
Predict the charge on each sphere.
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.
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.
Calculate the electric potential at O.
Sketch, on the axes, the variation of the electric potential V with distance between X and Y.
Identify the direction of the resultant force acting on Z as it oscillates.
Deduce whether the motion of Z is simple harmonic.