A dielectric object that has a quasi-permanent polarization when the applied field is zero is called an "electret" (electric equivalent of magnet). Consider a uniformly polarized electret in the shape of a cylinder of height h and radius 10h. The polarization in the dielectric is ^, where ^ is parallel to the cylinder axis.

(a) Calculate the electric field E at the center of the cylinder (since the radius is much larger than the height, the edge effects can be neglected)

(b) Calculate the electric field E on the midplane of the cylinder, at a distance 100h from the center. (Since distance is large compared to the radius, the dipole term dominates the potential).