## Question

An e.m.f. is induced in a coil placed in a changing magnetic field. The flux density B of this field varies with time as shown below.

At which value of t is the magnitude of the e.m.f. induced in the wire a maximum?

A) 1 ms

B) 2 ms

C) 3 ms

D) 4 ms

## Answer

The induced e.m.f. is given by the formula:

Hence the magnitude of the induced e.m.f. is given by:

This means that the induced e.m.f. will be the greatest when the rate of change of the magnetic flux density is the greatest.

From the graph, the rate of change of the magnetic flux density is the greatest when the gradient of the graph is the greatest.

This means that the induced e.m.f. will be the greatest at time t = 0 ms and t = 4 ms.

Hence the answer is D.