1. 1
   A flat square coil of 200 turns, each of side 5.0 cm, is placed in a uniform magnetic field of flux density 0.40 T. At first the normal to the plane of the coil makes an angle of 60° with the field. The coil is then turned steadily, in 0.050 s, until its normal is parallel to the field.

   (a)

   What is the magnetic flux through one turn of the coil in its initial position?

   [1 mark]

   • A0.10 Wb
   • B8.7 × 10⁻⁴ Wb
   • C1.0 × 10⁻³ Wb
   • D5.0 × 10⁻⁴ Wb

   (b)

   What is the average emf induced in the coil while it is turned?

   [1 mark]

   • A0.010 V
   • B0.54 V
   • C2.0 V
   • D4.0 V

   (c)

   The coil is connected to a resistor. Explain, using Lenz's law, the direction of the magnetic field produced by the induced current while the coil is being turned.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A metal rod of length 0.25 m rests across two horizontal parallel rails that are joined at one end by a 0.50 Ω resistor. A uniform vertical magnetic field of flux density 0.60 T acts over the whole arrangement. A force is applied to pull the rod along the rails at a constant 3.0 m s⁻¹, perpendicular to the field. The resistance of the rod and rails and all friction are negligible.

   (a)

   What is the emf induced across the rod?

   [1 mark]

   • A0.045 V
   • B0.45 V
   • C0.90 V
   • D7.2 V

   (b)

   Why must a force be applied to keep the rod moving at constant speed?

   [1 mark]

   • AThe induced current in the rod experiences a magnetic force that opposes its motion
   • BThe induced emf accelerates the rod, so a force is needed to hold its speed down
   • CEnergy dissipated in the resistor pushes the rod backwards
   • DA magnetic field exerts a force on any moving metal, even when no current flows

   (c)

   Show that the rate at which the applied force does work equals the rate at which energy is dissipated in the resistor.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student investigates a simple generator: a rectangular coil rotates at a steady frequency in a uniform magnetic field about an axis perpendicular to the field. She observes that the output emf varies sinusoidally with time and is zero at the instants when the plane of the coil is perpendicular to the field. She then changes only the frequency of rotation and records the peak emf: 1.6 V at 10 Hz, 3.2 V at 20 Hz and 4.8 V at 30 Hz.

   (a)

   Explain why the emf is zero when the plane of the coil is perpendicular to the field and is at its maximum when the plane of the coil is parallel to the field.

   [3 marks]

   (b)

   Deduce the relationship between peak emf and frequency, and predict the peak emf and the period of the emf when the coil rotates at 45 Hz.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A strong cylindrical magnet of mass 20 g is dropped from rest down three vertical tubes, each 1.0 m long and slightly wider than the magnet. It falls through a plastic tube in 0.45 s, through a copper tube with a narrow slit cut along its whole length in 0.9 s, and through a solid copper tube in 6.2 s. In the solid copper tube it falls at an almost constant speed for nearly all the way. Take g = 9.81 m s⁻².

   (a)

   Explain the three different fall times using Faraday's law and Lenz's law.

   [6 marks]

   (b)

   Discuss how the energy transfers for the magnet falling through the solid copper tube show that Lenz's law is a consequence of the conservation of energy.

   [6 marks]

   Total for question 4: 12 marks

End of questions