Question

A circular coil has a radius r and N turns and is in a uniform magnetic field that depends only on time, B = B(t). The angle of the coil is θ to the direction of the field and the total curcuit has resistance R. Find an expression for the current I.

Answer 1

(N x π x r^2 x Cosθ) / R x dB(t) / dt

Step-by-step explanation:

radius = r , Number of turns = N, B = B(t), Angle = θ, Resistance = R

induced emf = rate of change of magnetic flux

e = - N x dΦ / dt

e = - N x d(B A Cosθ) / dt

e = - N x A x Cosθ x dB(t) / dt

e = - N x π x r^2 x Cosθ x dB(t) / dt

where, negative sign shows the direction of induced emf in the coil.

induced current, i = induced emf / resistance

i = - (N x π x r^2 x Cosθ) / R x dB(t) / dt