Point dipole embedded in dielectric sphere

[erogard]

Homework Statement

A point dipole p is embedded at the center of a sphere of linear dielectric material (with radius R and dielectric constant $$\epsilon_{r}$$). Find the electric potential inside and outside the sphere.

Homework Equations

Well I'm guessing that using the method of separation of variables might be appropriate - my concern is to determine what "produces" the resulting potential. I would consider the embedded dipole as a free charge and go from there, but not sure what the resulting polarization might be.
Also: $$\rho_{b} = - ( \frac{ \chi_{e} }{1+\chi_{e} } ) \rho_{f}$$
Bound charge density is proportional to free charge density (here the embedded dipole).

The Attempt at a Solution

I know how to proceed once I get my boundary conditions set up; but that's my problem at the moment. Any hint would be greatly appreciated.

 

[jerrynoel]

Potential due to dipole + that of polarization?