Question

There are two concentric rings of 0.5 cm and 50 cm. The first one has a resistance of 5 Ohms and both are in the same plane. The large ring has a current of 3 Amps clockwise. After 0.2 seconds this one carries a current of 5 Amperes in the opposite sense to the hands of the clock. Answer the following questions:
a) What is the magnitude of the fem induced during the aforementioned period?
b) What is the magnitude and direction of the current produced in the small ring during the transition?
c) What is the magnitude and direction of the electric field that occurs in the small ring?

Answer 1

(a)

Assume magnetic field is uniform over the smaller ring which is 100 times smaller. EMF induced by Faraday's law

Thus,

R and r are the radius of larger and smaller circle respectively. There is a + sign because the final and initial current are in the opposite direction. Put in the values

(b)

Using, Lenz's law the current flows in the clockwise direction.

(c)

This again requires Faraday's law, in the following form

The electric field induced will be clockwise and a circular one along smaller circle. We already know RHS=E_emf , then by symmetry