Question

A circular coil of 312 winds of wire (radius = 7.0 cm, resistance = 7.4 Ω) is placed in a uniform magnetic field that is perpendicular to the plane of the loop. The magnitude of the field changes with time according to ? = 90sin(7?) mT, where ? is measured in seconds. Determine the magnitude of the current induced in the loop at ?=?/7 s.

Answer 1

Given :

No of turns = N = 312

radius of loop = r = 7 cm = 0.07 m

resistance = R = 7.4 ohm

magnetic field = B = 90sin(7t) mT = 0.09sin(7t) T

Magnetic flux through 1 turn of coil = B x area = B x r2

Total flux= = N x B x r2 = Nxr2 x 0.09 sin(7t)

E.m.f induced = E =

=> E = |7 x Nxr2 x 0.09 cos (7t) |

at t = /7 s,

E = |7 x Nxr2 x 0.09 cos (7x/7 ) | = 3.02 V

Therefore, Current Induced = E/R = 3.02/7.4 = 0.41 A.