Question

9. A small circular loop of area A is placed in the plane of, and concentric with, a large circular loop of radius R. Over the time interval from t = 0 to t = 1 s, the current in the large loop is reversed from +i, to -1, (a change in direction) at a constant rate according to i(t) = 1,(1 - 2t). The magnetic field Blarge loop produced by the large loop may be assumed to be constant over the area A of the small loop and equal to its value at the centre of the large loop. (a) Find the magnitude and direction of the emf induced in the small loop during this reversal. (b) Plot the flux (t) and the induced emf ind() as a function of t.

Answer 1

The magnetic field at the center of the large loop is

B= Hol 2R

or

B = Holo(1 – 2t) 2R

the flux through the small loop is magnetic fied times area of the small loop

D = BA-HO 410(1 - 2t) 2R

the magntitude of emf induced is

E=- do - Motio d(2t - 1) = MALO = 2R 2

which is constant.

If the current in the large loop changes from counterclockwise direction to clockwise direction, then the emf induced in the small loop is in the counterclockwise direction.

b) The plots are shown below

FLux vs t is shown below

Flux 0.2 0.6 0.8

The emf vs t is shown below

om 02 04 0.6 0.8 1.0