Question

Consider a circular coil of radius 13.8 cm and consisting of 11 turns. The coil is placed in a varying magnetic field that changes uniformly from 5.34 T to 2.7 T in an interval of 12 seconds. If the axis of the coil makes an angle of 13^O to the magnetic field:

a) Calculate the induced emf in the coil.

b) If the angle that the coil makes with the magnetic field is charge to 67.4^O, what would the radius need to be for the emf to remain the same?

Answer 1

given
r = 13.8 cm = 0.138 m
N = 11 turns
B1 = 5.34 T
B2 = 2.7 T
t = 12 seconds

theta = 13 degrees

a) induced emf in the coil = N*A*(B1 - B2)*cos(theta)/t

= 11*pi*0.138^2*(5.34 - 2.7)*cos(13)/12

= 0.141 V <<<<<<<<---------------Answer

b) let r' is the radius needed.

induced emf when r is 13.8 cm = induced emf is r'

N*A*(B1 - B2)*cos(13)/t = N*A'*(B1 - B2)*cos(67.4)/t

pi*r^2*cos(13) = pi*r'^2*cos(67.4)

r' = r*sqrt(cos(13)/cos(67.4) )

= 13.8*sqrt(cos(13)/cos(67.4) )

= 22.0 cm (or) 0.220 m <<<<<<<<---------------Answer