Electric field inside an electret

[rockbreaker]

Homework Statement

I would like to refer to this problem about the electric field inside an electret. https://www.physicsforums.com/showthread.php?t=444106
An elecret is a dielectric that has a quasi-permanent polarization when there is no applied field. Consider a uniformly polarized cylindrical electret. The cylinder has a radius of 10h and a length h. The polarization is Pk where k is a unit vector along the axis.

a. Draw the electric field lines. (Done)
b. Calculate the electric field at the center of the cylinder. Ignore edge effects.
c. Calculate the electric field on the midplane of the cylinder at a distance
100h from the center. The approximation of a point dipole can be used since the distance is very large.

Homework Equations

D=ε0*E+P
D=εE

The Attempt at a Solution

I want to calculate the electric field inside the electret. P is given, but I miss D to be able to calculate E. Can someone give me a hint how to advance? I guess I have to start with calculating σb=P*n. Is then E the volume integral over σb?

 

[rockbreaker]

b) As there are no other charges involved, I think the field inside the electret is
σB=P*n=-P
E=σ/ε0=σb/ε0=-P/ε0

For c), I would like to use the expansion of the potential, V=1/4∏ε0*(Q/r+r*p/r^2), where the dipole term dominates because we are far away from the electret. But isn't r*p=0 (scalar product) although the field mustn't be 0 there?