3-1. In each of the cases below, find the bound surface and volume charge densities $\rho_{ps}$, $\rho_{pv}$. In
addition, show that the dielectric is electrically neutral, i.e, that the total bound charge is zero.
(a) A uniformly polarized cylinder of length $l$ and radius $a$:
$\vec{P} = \hat{a}_z P_0$ ($0 < \rho < a$, $-\frac{l}{2} < z < \frac{l}{2}$)
(b) A uniformly polarized sphere of radius $a$:
$\vec{P} = \hat{a}_z P_0$ ($r < a$)
(c) A radially polarized cube of side $l$, centered at the origin:
$\vec{P} = (\hat{a}_x x + \hat{a}_y y + \hat{a}_z z) P_0$
