Electric Field inside and outside of Dielectric sphere

JayKo

1. The problem statement, all variables and given/known data

A dielectric sphere of radius R has a uniform permanent polarisation P. Determine the electric field both inside and outside the sphere. (Hint: Since div P = 0 everywhere, the electrostatic potential satisfies Laplace's equation. Do not assume that the sphere is characterised by a dielectric constant. Instead, use D = [tex]\epsilon_{0}[/tex]E₀ + P.)

2. Relevant equations

use the laplace equation where the general form of potential is:
[tex]V=\Sigma (A_{l}r^{l}P_{l}(cos(theta))+B_{l}*1/(r_{l+1})*P_{l}(cos(theta)))[/tex]

3. The attempt at a solution

set the boundary condition when outside of sphere :
r ->infinity, V->0 hence A_l=0

when inside the sphere
r-> 0, V not= infinity hence B_l=0

the next time is to find both the coefficients, a.k.a A_l and B_l. so far am i heading the right directions?


my question is also what D = [tex]\epsilon_{0}[/tex]E₀ + P purpose here in solving this problem?