A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity co 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. 5.57).
(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).
(e) Find the magnetic field at a point (r, θ) inside the sphere, and check that it is consistent with (b).