Imagine an iron sphere of radius R that carries a charge Q and a uniform magnetization M = Mz. The sphere is initially at rest.

(a) Compute the angular momentum stored in the electromagnetic fields.

(b) Suppose the sphere is gradually (and uniformly) demagnetized (perhaps by heating it up past the Curie point). Use Faraday's law to determine the induced electric field, find the torque this field exerts on the sphere, and calculltte the total angular momentum imparted to the sphere in the course of the demagnetization.

(c) Suppose instead of demagnetizing the sphere we discharge lt, by connecting a grounding wire to the north pole. Assume the current flows over the surface in such a way that the charge density remains uniform. Use the Lorentz force law to determine the torque on the sphere, and calculate the total angular momentum imparted to the sphere in the course of the discharge. (The magnetic field is discontinuous at the surface... does this matter?)