Question

A uniformly charged solid sphere of mass m, radius r having charge q is rotated about its diameter with frequency f0. The magnetic moment of the sphere is

Answer 1

we know, moment of inertia of sphere about its diameter, I = 2/5 mr²

where m is mass of sphere and r is the radius of the sphere.

now, angular momentum, L = I × w

where w is angular frequency,

we know, w = 2πf0

so, angular momentum, L = 2/5 mr² × 2πf0

= 4/5 πmr²f0 ........(1)

now, magnetic moment/angular momentum = charge/2 × mass

so, magnetic moment = (charge /2 × mass ) × angular momentum

= q/2m × 4/5 πmr²f0

= 2/5 πqr²f0

hence, magnetic moment of the sphere is 2/5 πqr²f0