Question

A charge q is uniformly distributed over the volume of a uniform ball of mass m and radius R which rotates with an angular velocity ω about the axis passing through its centre. Find the respective magnetic moment and its ratio to the mechanical moment.

Answer 1

The magnetic moment must clearly be along the axis of rotation. Consider a volume element dV. It contains a charge  The rotation of the sphere causes this charge to revolve around the axis and constitute a current.