In the figure below a very small circular metal ring of radius r = 0.5 cm and re
ID: 2037776 • Letter: I
Question
In the figure below a very small circular metal ring of radius r = 0.5 cm and resistance x-5 ? is at the center of a large concentric circular metal ring of radius R = 50 cm. The two rings lie in the same plane. At t = 5 s, the large ring carries a clockwise current of 3 A. At t = 5.2 s, the large ring carries a counterclockwise current of 5 A. 50 cm 0.5 cm 5 2 (a) What is the magnitude of the emf in the small ring during this time? 9.869604404e-8 (b) What are the magnitude and direction of the average current in the small ring? 1.973920881e-8 magnitude direction Clockwie (c) What is the average electric field in the small ring during this time? Give both the magnitude and direction of the electric field. 56797.15533 V/m directionClockwiseExplanation / Answer
a) magnetic field at the center of the small ring due to large ring,
B = mue*I/(2*R)
induced emf in the small ring = A*(B2 - B1)/t
= pi*r^2*mue*(I2 - I1)/(2*R*t)
= pi*(0.5*10^-2)^2*4*pi*10^-7*(5 - (-3))/(2*0.5*0.2)
= 3.95*10^-9 V
b) induced current = induced emf/R
= 3.95*10^-9/5
= 7.89*10^-10 A
direction : clockwise
c) E = induced emf/(2*pi*R)
= 3.95*10^-9/(2*pi*0.5)
= 1.26*10^-9 V/m
direction : clockwise