A small circular loop with area A is placed in the plane of, and concentric with
ID: 1507229 • Letter: A
Question
A small circular loop with area A is placed in the plane of, and concentric with, a large circular loop with radius R. The current in the large loop is changed at a constant rate from i to -i (a change in direction) over a time t. 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) time 0 (the instant the current begins to change), (b) time t/2 , and (c) at time t? (d) What is the magnitude of the emf () induced in the small loop while the current in the large loop is changing? Assume this inner loop is much smaller than the outer loop so that the magnetic field is uniform over its area. State your answers in terms of the given variables, using 0 when needed.
Explanation / Answer
a)
at t= 0 ,
current = i
B = 0*Current / (2*R)
= 0*i/(2*R)
b)
at t= t/2 ,
current = 0
B = 0*Current / (2*R)
= 0*0/(2*R)
= 0
c)
at t= t ,
current = -i
B = 0*Current / (2*R)
= -0*i/(2*R)
d)
di/dt = -2i/t
E = -A*dB/dt
= -A*(0/2R)*di/dt
= -A*(0/2R)*(-2i/t)
= 2*A*i*0 / 2R
A is rea of smaller loop