Question

The mutual inductance between a long insulated coil wrapped around a solenoid is 4.0 x 10-4 H.
If the current in the solenoid drops at a constant rate from 15.0 A to zero in 0.076 s, what is the
magnitude of the emf induced in the coil?

Answer 1

Solution

We know from the theory of mituam induction, the e.m.f induced in a nearby circuit can be given by the formula,

Induced e.m.f,

Where M is the mutual inductance between the loops and dI/dt is the rate of change of current in the loop. The negative sign shows that the induced e.m.f flows in the circuit such a way that it will oppose the change producing it. Here we are not concerned with the direction of current flow hence we will be talking only about magnitude of induced e.m.f.

Now given the value of mutual inductance, M=4*10-4H

We need to calculate dI/dt. Given that the current steadily decreases from 15A to 0A within 0.076 seconds. Hence the constant value of dI/dt can be calculated as,

Thus we can calculate the induced e.m.f as,

Thus the magnitude of induced e.m.f is 0.0789V