Question

A rectangular coil with N turns and dimensions a and b swings with small amplitude suspended pendulum-like from the side of length b. It has a total resistance R. The coil has moment of inertia I and is immersed in a vertical magnetic field of magnitude B. Find a formula for the current in the coil as a function of time

(a.) condidering only the gravitational torque on the coil,

(b.) considering both the gravitational and the magnetic torque.

Answer 1

a) condidering only the gravitational torque on the coil

=> N * i * (a * b) * B =   (m * g) * b

=>    current in coil = (m * g)/(N * a * B)

b)    considering both the gravitational and the magnetic torque

induced emf = N * B * (a * b)/t

=>     i   =   N * B * (a * b)/(Rt)