Electrodynamic - Spherical cavity in dielectric

[emeriska]

First, sorry if something is not totally clear, I'm translating physics term the best I can!

1. Homework Statement
A sphere or radius a of permittivity ε₂ is placed in a dielectric ε₁. Without the sphere, we would have E = E₀. We want to find the solution to this problem when ε₂ = 1 (vacuum).

Homework Equations

Seems like I'll need those test functions:
V₁=-E₀ + p/r³ (when r > a)
V₂=-E₂ (when r < a)

The Attempt at a Solution

I figured I'll need density of charge of polarization at the surface and the field produced by these charges.

So now the thing is my last electrodynamic course was a loonng time ago and I'd kinda need a head start on this one. I'm looking through the Griffith but I can't seem to find anything to help me get this problem started.

If you guys have any ideas of links that might help that'd be great! Thanks!

 

[TSny]

Since you have Griffiths, look at the section titled "Boundary Value Problems with Linear Dielectrics". In the the 3rd edition, it is section 4.4.2. There is an example problem that is similar to (but not the same as) your problem.