How Does the Method of Images Determine Potential Inside a Grounded Sphere?

[crimsonidol]

Homework Statement

We have a grounded conducting sphere of radius R and a charge q is placed a distance a from the center of the sphere. Show that the potential in the interior produced by q and the distributed induced charge is the same as that produced by q and its image charge q'.The image charge is at a distance a'=R^2/a fro the center collinear with q and the origin. Calculate the electrostatic potential for a<R<a'. Show that potential vanishes for r=R if we take q'=-qR/a

Homework Equations

In the course we are investigating legendre equations, legendre polynomials etc.

The Attempt at a Solution

I can find potential by simply using V=Sum (1/4pieps)q/r however there is no legendre polynomial or legendre series in it. I tried Laplace's Equation however I got confused. Because in Laplace's eqn I can only deal with r. Where have I gone wrong? How should i think?

 

[crimsonidol]

I just need a spark?

 

[ehild]

Read this. http://en.wikipedia.org/wiki/Method_of_image_chargesehild

 

[crimsonidol]

I know that solution, however there is nothing related to legendre in it. The question was given to me as a homework for Legendre equation/polynomials topic. I should o something related to that I suppose.