A uniformly charged solid sphere of radius R carries a

QUESTION:

Problem 60P

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).

Reference Ex. 5.11.]

A spherical shell of radius R, carrying a uniform surface charge σ, is set spinning at angular velocity ω. Find the vector potential it produces at point r (Fig. 5.45).