Question

A small circular loop of area 2.20 cm2 is placed in the plane of, and concentric with, a large circular loop of radius 1.23 m. The current in the large loop is changed at a constant rate from 219 A to -219 A (a change in direction) in a time of 1.14 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 = 0.570 s, and (c) t = 1.14 s? (d) From t = 0 to t = 1.14 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 = 0.570 s?

Answer 1

given

dI/dt = (-219-219)/1.14 = -384.2

dI = -384.2*dt

I = integral dI

I = Io - 384.2*t

Io = 219 A

I = 219 - 384.2*t

magnetic field B due to large loop B = uo*I/(2R)

part(a)

at t = 0

I = 219

B = 4*pi*10^-7*219/(2*1.23)

B = 1.1*10^-4 T

part(b)

at t = 0.57 s

I = 219 - (384.2*0.57) = 0.006 A

B = 4*pi*10^-7*0/(2*1.23)

B = 0

part(c)

at t = 1.14 s

I = 219 - 384.2*1.14 = -219 A

B = -4*pi*10^-7*219/(2*1.23)

B = -1.1*10^-4 T

B is reversed

part(d)

flux = B*A = uo*I*A/(2R) = ( A*uo/2R)*(Io - 384.2*t)

EMF = -(d/dt)*flux

EMF = ( A*uo/2R)*384.2

emf = 2.2*10^-4*4pi*10^-7*384.2/(2*1.23)

emf = 4.32*10^-8 T