20. Magnetic fields
A section of Physics, 9702
Listing 10 of 214 questions
A coil of wire is situated in a uniform magnetic field of flux density B. The coil has diameter 3.6 cm and consists of 350 turns of wire, as illustrated in . 3.6 cm coil, 350 turns uniform magnetic field flux density B The variation with time t of B is shown in . B / mT t / s 0.2 0.4 0.6 0.8 Show that, for the time t = 0 to time t = 0.20 s, the electromotive force (e.m.f.) induced in the coil is 0.080 V. On the axes of , show the variation with time t of the induced e.m.f. E for time t = 0 to time t = 0.80 s. –0.1 –0.2 0.1 0.2 0.2 0.4 0.6 0.8 E / V t / s A bar magnet is held a small distance above the surface of an aluminium disc by means of a rod, as illustrated in . rotating magnet fixed aluminium disc The aluminium disc is supported horizontally and held stationary. The magnet is rotated about a vertical axis at constant speed. Use laws of electromagnetic induction to explain why there is a torque acting on the aluminium disc.
9702_s20_qp_41
THEORY
2020
Paper 4, Variant 1
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A coil of wire is situated in a uniform magnetic field of flux density B. The coil has diameter 3.6 cm and consists of 350 turns of wire, as illustrated in . 3.6 cm coil, 350 turns uniform magnetic field flux density B The variation with time t of B is shown in . B / mT t / s 0.2 0.4 0.6 0.8 Show that, for the time t = 0 to time t = 0.20 s, the electromotive force (e.m.f.) induced in the coil is 0.080 V. On the axes of , show the variation with time t of the induced e.m.f. E for time t = 0 to time t = 0.80 s. –0.1 –0.2 0.1 0.2 0.2 0.4 0.6 0.8 E / V t / s A bar magnet is held a small distance above the surface of an aluminium disc by means of a rod, as illustrated in . rotating magnet fixed aluminium disc The aluminium disc is supported horizontally and held stationary. The magnet is rotated about a vertical axis at constant speed. Use laws of electromagnetic induction to explain why there is a torque acting on the aluminium disc.
9702_s20_qp_43
THEORY
2020
Paper 4, Variant 3
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State Faraday’s law of electromagnetic induction. shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil. V coil magnetic field The coil is connected to a centre-zero voltmeter. The flux density B of the uniform magnetic field varies with time t as shown in . t / ms B / mT The coil consists of 340 turns, each of cross-sectional area 3.2 × 10–4 m2. Calculate the maximum magnetic flux through one turn of the coil. maximum magnetic flux = Wb Determine the maximum rate of change of magnetic flux linkage in the coil. maximum rate of change of flux linkage = Wb s–1 State the maximum electromotive force (e.m.f.) V0 induced across the coil. V0 = V On , sketch the variation of the e.m.f. V induced across the coil with t from t = 0 to t = 6.0 ms. –V0 V0 V t / ms The variation of V with t can be described by V = A sin Bt where A and B are constants. Determine the values of A and B. Give units with your answers. A = unit B = unit , ,
9702_s24_qp_42
THEORY
2024
Paper 4, Variant 2
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A bar magnet is suspended vertically from the free end of a helical spring, as shown in . V helical spring magnet coil One pole of the magnet is situated in a coil. The coil is connected in series with a high-resistance voltmeter. The magnet is displaced vertically and then released. The variation with time t of the reading V of the voltmeter is shown in . 0.5 1.0 1.5 2.0 2.5 t / s V State Faraday’s law of electromagnetic induction. Use Faraday’s law to explain why 1. there is a reading on the voltmeter, 2. this reading varies in magnitude, 3. the reading has both positive and negative values. Use to determine the frequency f0 of the oscillations of the magnet. f0 = Hz The magnet is now brought to rest and the voltmeter is replaced by a variable frequency alternating current supply that produces a constant r.m.s. current in the coil. The frequency of the supply is gradually increased from 0.7 f0 to 1.3 f0, where f0 is the frequency calculated in . On the axes of , sketch a graph to show the variation with frequency f of the amplitude A of the new oscillations of the bar magnet. 0.7 f0 A f0 1.3 f0 f Name the phenomenon illustrated on your completed graph of . State one situation where the phenomenon named in is useful.
9702_s11_qp_42
THEORY
2011
Paper 4, Variant 2
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A bar magnet is suspended vertically from the free end of a helical spring, as shown in . V helical spring magnet coil One pole of the magnet is situated in a coil. The coil is connected in series with a high-resistance voltmeter. The magnet is displaced vertically and then released. The variation with time t of the reading V of the voltmeter is shown in . 0.5 1.0 1.5 2.0 2.5 t / s V State Faraday’s law of electromagnetic induction. Use Faraday’s law to explain why 1. there is a reading on the voltmeter, 2. this reading varies in magnitude, 3. the reading has both positive and negative values. Use to determine the frequency f0 of the oscillations of the magnet. f0 = Hz The magnet is now brought to rest and the voltmeter is replaced by a variable frequency alternating current supply that produces a constant r.m.s. current in the coil. The frequency of the supply is gradually increased from 0.7 f0 to 1.3 f0, where f0 is the frequency calculated in . On the axes of , sketch a graph to show the variation with frequency f of the amplitude A of the new oscillations of the bar magnet. 0.7 f0 A f0 1.3 f0 f Name the phenomenon illustrated on your completed graph of . State one situation where the phenomenon named in is useful.
9702_s11_qp_43
THEORY
2011
Paper 4, Variant 3
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A bar magnet of mass 250 g is suspended from the free end of a spring, as illustrated in . spring magnet coil The magnet hangs so that one pole is near the centre of a coil of wire. The coil is connected in series with a resistor and a switch. The switch is open. The magnet is displaced vertically and then allowed to oscillate with one pole remaining inside the coil. The other pole remains outside the coil. At time t = 0, the magnet is oscillating freely as it passes through its equilibrium position. At time t = 6.0 s, the switch in the circuit is closed. The variation with time t of the vertical displacement y of the magnet is shown in . –2.0 –1.5 –1.0 –0.5 0.5 1.0 y / cm 1.5 2.0 t / s For the oscillating magnet, use data from to calculate, to two significant figures, the frequency f, f = Hz the energy of the oscillations during the time t = 0 to time t = 6.0 s. energy = J State Faraday’s law of electromagnetic induction. Use Faraday’s law and energy conservation to explain why the amplitude of the oscillations of the magnet reduces after time t = 6.0 s.
9702_s17_qp_42
THEORY
2017
Paper 4, Variant 2
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State, by reference to the power dissipated in a resistor, what is meant by the root-mean-square (r.m.s.) value of an alternating voltage. A coil is rotating freely, on frictionless bearings, at constant speed in a uniform magnetic field. This rotation causes an induced alternating electromotive force (e.m.f.) across the open terminals of the coil. The induced e.m.f. has r.m.s. value 12 V and frequency 50 Hz. The speed of rotation of the coil is now doubled. State and explain, with reference to the principles of electromagnetic induction, the effect of the increased speed of rotation on the r.m.s. value of the induced e.m.f. On , sketch the variation with time t of the induced e.m.f. E across the terminals of the coil at the increased speed of rotation. Your line should extend from time t = 0 to time t = 20 ms. Assume that E = 0 when t = 0. –40 –20 E / V t / ms State and explain the effect on the motion of the coil in of connecting a load resistor across its terminals.
9702_w21_qp_41
THEORY
2021
Paper 4, Variant 1
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State, by reference to the power dissipated in a resistor, what is meant by the root-mean-square (r.m.s.) value of an alternating voltage. A coil is rotating freely, on frictionless bearings, at constant speed in a uniform magnetic field. This rotation causes an induced alternating electromotive force (e.m.f.) across the open terminals of the coil. The induced e.m.f. has r.m.s. value 12 V and frequency 50 Hz. The speed of rotation of the coil is now doubled. State and explain, with reference to the principles of electromagnetic induction, the effect of the increased speed of rotation on the r.m.s. value of the induced e.m.f. On , sketch the variation with time t of the induced e.m.f. E across the terminals of the coil at the increased speed of rotation. Your line should extend from time t = 0 to time t = 20 ms. Assume that E = 0 when t = 0. –40 –20 E / V t / ms State and explain the effect on the motion of the coil in of connecting a load resistor across its terminals.
9702_w21_qp_43
THEORY
2021
Paper 4, Variant 3
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An ideal transformer is shown in . primary coil 1200 turns secondary coil input output core Explain why the core is made of iron, why an electromotive force (e.m.f.) is not induced at the output when a constant direct voltage is at the input. An alternating voltage of peak value 150 V is applied across the 1200 turns of the primary coil. The variation with time t of the e.m.f. E induced across the secondary coil is shown in . –20 E / V –40 –60 5.0 10.0 15.0 20.0 25.0 t / ms Use data from to calculate the number of turns of the secondary coil, number = state one time when the magnetic flux linking the secondary coil is a maximum. time = ms A resistor is connected between the output terminals of the secondary coil. The mean power dissipated in the resistor is 1.2 W. It may be assumed that the varying voltage across the resistor is equal to the varying e.m.f. E shown in . Calculate the resistance of the resistor. resistance = Ω On , sketch the variation with time t of the power P dissipated in the resistor for t = 0 to t = 22.5 ms. 1.0 2.0 3.0 5.0 10.0 15.0 20.0 25.0 P / W t / ms
9702_m17_qp_42
THEORY
2017
Paper 4, Variant 2
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Use A magnet is suspended vertically from a fixed point by means of a spring, as shown in . spring coil magnet R One end of the magnet hangs inside a coil of wire. The coil is connected in series with a resistor R. The magnet is displaced vertically a small distance D and then released. shows the variation with time t of the vertical displacement d of the magnet from its equilibrium position. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 +D –D d t /s Examiner’s Use State and explain, by reference to electromagnetic induction, the nature of the oscillations of the magnet. Calculate the angular frequency ω0 of the oscillations. ω0 = …………….……………… rad s–1 The resistance of the resistor R is increased. The magnet is again displaced a vertical distance D and released. On , sketch the variation with time t of the displacement d of the magnet. Examiner’s Use The resistor R in is replaced by a variable-frequency signal generator of constant r.m.s. output voltage. The angular frequency ω of the generator is gradually increased from about 0.7ω0 to about 1.3ω0, where ω0 is the angular frequency calculated in . On the axes of , sketch a graph to show the variation with ω of the amplitude A of the oscillations of the magnet. A 0.7 0 1.0 0 1.3 0 ω ω ω ω State the name of the phenomenon illustrated in the graph of . Briefly describe one situation where the phenomenon named in is useful and one situation where it should be avoided. useful: avoid:
9702_s07_qp_4
THEORY
2007
Paper 4, Variant 0
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Questions Discovered
214