Potential inside a grounded conducting sphere

[shinobi20]

Homework Statement

Hi, I'm currently answering a problem in Jackson's electrodynamics. The question is:
Given a point charge q inside a hollow. grounded, conducting sphere of inner radius a. Find the potential inside.

This can be solved by placing an image charge outside the sphere, and placing q a distance say, r from the center. I'm just wondering, what if the charge is exactly at the center of the sphere? What changes in the solution would happen?

Homework Equations

Method of Images

The Attempt at a Solution

 

[BvU]

Well, what happens to the image charge if q approaches the center ?

 

[shinobi20]

The image charge approaches infinity. But how will I modify the solution?

 

[shinobi20]

Well, what happens to the image charge if q approaches the center ?

How is the Green function to be used here? I think this is a possible way but I'm not sure.

 

[BvU]

The image charge approaches infinity. But how will I modify the solution?

Very good. Now imagine q is distributed over 100 little charges that are evenly distributed on a small spherical shell around the center. That gives 100 image charges evenly distributed very far away, right ?

See where I am going ?

How is the Green function to be used here? I think this is a possible way but I'm not sure.

I'm not much good with these (very useful) functions, so I try to wiggle around them