Compare Eqs. 2.15, 4.9, and 6.11. Notice that if p, P, and M are uniform, the same integral is involved in all three: Therefore, if you happen to know the electric field of a uniformly charged object, you can immediately write down the scalar potential of a uniformly polarized object, and the vector potential of a uniformly magnetized object, of the same shape. Use this observation to obtain V inside and outside a uniformly polarized sphere (Ex. 4.2), and A inside and outside a uniformly magnetized sphere (Ex.6.1).

1 dr'.