A cylinder of length 2L has its axis along the z-axis and a circular cross section of radius a. The origin is at the center of the cylinder that is uniformly polarized in the direction of the axis, that is, P = pz^ where p = const.
a) Find the bound charge densities pro(b) and sigma(b).
b) Find the electric field for all points on the z-axis for which z >= 0.
c) Verify that your result in (b) satisfies the boundary condition at z = L.
d) From the result of (b), find E at the origin.