Electromagnetic Induction — Practice

Question 1

A coil of area 0.05 m squared is placed with its plane perpendicular to a field of 0.4 T. Find the flux through it.

Accepted Answer

With the plane perpendicular to B the normal is along B, so theta is zero and the cosine is one. Answer: Flux = 0.02 Wb.

Question 2

The flux through a 200-turn coil falls from 0.06 Wb to 0.02 Wb in 0.1 s. Find the average induced emf.

Accepted Answer

Apply emf = N times the change in flux divided by the time, taking the magnitude. Answer: emf = 80 V.

Question 3

A rod of length 0.5 m moves at 4.0 m/s perpendicular to a field of 0.30 T. Find the emf across its ends.

Accepted Answer

Use emf = B l v, valid because the motion is perpendicular to both the rod and the field. Answer: emf = 0.6 V.

Question 4

A rod of length 0.8 m rotates about one end at 50 rad/s in a field of 0.20 T normal to its plane of rotation. Find the emf between the ends.

Accepted Answer

The speed varies along the rod, so integrate to get half B omega l squared. Answer: emf = 3.2 V.

Question 5

The current in a coil falls from 4.0 A to 0 in 0.05 s, inducing an average emf of 80 V. Find the self-inductance.

Accepted Answer

Rearrange emf = L times the rate of change of current, using magnitudes. Answer: L = 1.0 H.

Question 6

Two coils have a mutual inductance of 0.8 H. If the current in the first changes from 2.0 A to 6.0 A in 0.2 s, find the emf induced in the second and the change in flux linkage.

Accepted Answer

Use emf = M times the rate of change of current, and flux linkage change = M times the current change. Answer: emf = 16 V; change in flux linkage = 3.2 Wb.

Question 7

A solenoid 40 cm long with 800 turns and area 5.0 x 10^-4 m squared carries 2.0 A. Find its inductance and the energy stored.

Accepted Answer

First form n as turns per unit length, then use L = mu_0 n squared A l and U = half L I squared. Answer: L = 2.5 x 10^-3 H; U = 5.0 x 10^-3 J.

Question 8

A coil of 100 turns and area 0.02 m squared rotates at 50 rad/s in a field of 0.5 T. Find the peak emf and state the coil orientation at which it occurs.

Accepted Answer

Use peak emf = N B A omega, then recall which orientation makes the flux change fastest. Answer: Peak emf = 50 V, when the plane of the coil is parallel to the field.

Question 9

A bar magnet is moved away from a closed coil with its north pole facing the coil. State the direction of the induced current as seen from the magnet, and justify it by energy conservation.

Accepted Answer

Decide whether the flux is rising or falling, then choose the pole that opposes that change. Answer: Clockwise as seen from the magnet, forming a south pole that attracts the magnet and opposes its recession; work done against this attraction supplies the electrical energy.

Practice — Electromagnetic Induction

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