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- Homework Statement
- A point dipole p is imbedded at the center of a sphere of linear

dielectric material (with radius R and dielectric constant er). Find the electric potential inside and outside the sphere.

- Relevant Equations
- Laplace's equation

I tried to solve it for some time and then looked at the solution manual, which got me completely lost. Those are the first lines of the solution :

I'm not so sure how equation 4.39:

makes him conclude that the same relation holds for dipole moments. My second concern is that I'm not sure how he uses laplace's eauation when the center of the sphere has a dipole consisting of equal and opposite charges. How am I allowed to solve laplace's equation in places where there is charge? Also I'm not sure how he got the potential inside the sphere. Did he use the superposition of the dipole potential with that of the surface charge bound potential? Someone help me please

I'm not so sure how equation 4.39: