Induction practice questions.

A flat coil of area 0.050 m² is placed in a uniform magnetic field of flux density 0.60 T. The field makes an angle of 60° with the plane of the coil. The magnetic flux through the coil is:

• 0.015 Wb
• 0.052 Wb
• 0.026 Wb
• 0.030 Wb

Answer: 0.026 Wb

Flux uses the angle to the normal: the field is at 60° to the plane, so 30° to the normal, and Φ = BA cos30° = 0.60 × 0.050 × 0.866 = 0.026 Wb. Using cos60° instead is the classic error.

The north pole of a bar magnet is moved towards the face of a stationary conducting coil. According to Lenz's law, the face of the coil nearest the magnet becomes:

• a north pole, so that the approaching magnet is repelled
• a south pole, so that the approaching magnet is attracted
• alternately north and south as the magnet approaches
• unmagnetised, since the coil carries no current

Answer: a north pole, so that the approaching magnet is repelled

The induced current must oppose the change producing it, so the coil face repels the approaching north pole by becoming a north pole itself.

The magnetic flux through a coil increases at a constant rate for several seconds. During this time, the emf induced in the coil is:

• zero, because the flux is not oscillating
• constant and non-zero
• increasing at a constant rate
• sinusoidal

Answer: constant and non-zero

By Faraday's law the emf equals the rate of change of flux linkage. A constant rate of change gives a constant, non-zero emf — students often wrongly link emf to the flux itself rather than to its rate of change.

A given change of magnetic flux is applied to a coil. The number of turns of the coil is doubled and the same flux change now occurs in half the original time. Compared with the original induced emf, the new emf is:

• the same
• 2 times larger
• 4 times larger
• 8 times larger

Answer: 4 times larger

emf = NΔΦ/Δt. Doubling N doubles the emf, and halving the time doubles it again, giving a factor of 4.

A strong magnet is dropped down the inside of a long vertical copper tube. Compared with an identical fall through air alone, the magnet:

• falls at exactly the same rate, since copper is non-magnetic
• falls faster, because it is attracted downwards by the tube
• experiences no gravitational force inside the tube
• falls more slowly, because induced eddy currents oppose its motion

Answer: falls more slowly, because induced eddy currents oppose its motion

The moving magnet induces eddy currents in the tube walls; by Lenz's law these create forces opposing the magnet's motion, so it descends noticeably more slowly.

The magnetic flux linkage NΦ through a coil is plotted against time t. Which quantity is given by the magnitude of the gradient of this graph?

• The magnetic flux density through the coil
• The charge that has flowed through the coil
• The emf induced in the coil
• The current induced in the coil, in amperes

Answer: The emf induced in the coil

Faraday's law states ε = −d(NΦ)/dt, so the gradient of a flux-linkage against time graph is the induced emf. The induced current depends in addition on the resistance of the circuit, and the charge that flows is set by the change in flux linkage rather than by the rate at which it changes.