A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity ω about the z axis.
(a) What is the magnetic dipole moment of the sphere?
(b) Find the average magnetic field within the sphere (see Prob. 5.59).
(c) Find the approximate vector potential at a point (r,θ) where r≫R.
(d) Find the exact potential at a point (r,θ) outside the sphere, and check that it is consistent with (c). [Hint: refer to Ex. 5.11.]
(e) Find the magnetic field at a point (r,θ) inside the sphere (Prob. 5.30), and check that it is consistent with (b).