Electrostatic potential in Legendre polynomials

[technion]

Homework Statement

Two spherical shells of radius ‘a’ and ‘b’ (b>a) are centered about the origin of the
axes, and are grounded. A point charge ‘q’ is placed between them at distance R from the
origin (a<R<b).
Expand the electrostatic potential in Legendre polynomials and find the Green function of
the problem as a series. Explicitly find all pre-factors.

Homework Equations

The Attempt at a Solution

The potential on the outer shell is q/b and the inner shell q/R, right? How do I represent this in legendre polynomials?

 

[gabbagabbahey]

Hi technion, welcome to PF!

Is it safe to assume that the the shells are conductors? (You didn't tell us in your problem statement)

The potential on the outer shell is q/b and the inner shell q/R, right?

Well, what is your reasoning behind this?

How do I represent this in legendre polynomials?

What is the general expansion of the potential in terms of Legendre polynomials?