Unipolar Induction via a Rotating Magnetized Sphere

A neutral, conducting sphere of radius R with permanent magnetization density M0 = M0 ẑ parallel to its axis when at rest is rotated about that axis with angular velocity ω = ω z ̂ with respect to the lab frame. Deduce the electric-charge distribution, the electric potential and the electric field in the lab frame. Compare with the case that the sphere is nonconducting. This configuration is a variant of unipolar induction, as discussed by Faraday in 1851 [1], who also considered the case of the magnetized cylinder at rest while the voltmeter and contact wires rotated around the axis of the cylinder.1