Question

A small circular loop of area 2.34 cm² is placed in the plane of, and concentric with, a large circular loop of radius 1.22 m. The current in the large loop is changed at a constant rate from 203 A to -203 A (a change in direction) in a time of 1.17 s, starting at t = 0.What is the magnitude of the magnetic field at the center of the small loop due to the current in the large loop at (a) t = 0, (b) t = 0.585 s, and (c) t = 1.17 s? (d) From t = 0 to t = 1.17 s, is B reversed? Because the inner loop is small, assume is uniform over its area. (e) What emf is induced in the small loop at t = 0.585 s?

a) 1.04e-4 units T

b) units T

c) units T

e) units V

Answer 1

The magnetic field at the center of the loop is given by:

B = mu0 I / 2 R

at t = 0, I = 203 A

B = 4 pi x 10-7 x 203 / 2 x 1.22 = 1.044 x 10^-4 T

Hence, at t = 0 ; B = 1.044 x 10^-4 T

b)at t = 0.555 s, the current in the loop shpuld be 0 A hence the magnetic field will also be zero.

c)at t = 1.17 s, B field will be:

B = mu0 I / 2 R

at t = 1.11, I = 202 A

B = 4 pi x 10-7 x -203 / 2 x 1.22 = -1.044 x 10^-4 T

Hence, at t = 1.17 s ; B = - 1.044 x 10^^-4 T

d)Yes. As shown above its reversed. (- sign indicates that).