Electric Field inside and outside of Dielectric sphere

[JayKo]

Homework Statement

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 = \epsilon_{0}E₀ + P.)

Homework Equations

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

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 = \epsilon_{0}E₀ + P purpose here in solving this problem?

 

[kuruman]

There are two regions in space, one inside and one outside the sphere. Therefore, you need to consider two separate potentials, one inside and one outside, then match boundary conditions. That's where the equation $\mathbf{D}=\epsilon_0 \mathbf{E}+\mathbf{P}$ comes in.