# Image charge problem

1. Feb 2, 2016

### aaaa202

I suppose you are all familiar with the standard image charge problem of calculating the electric potential for a point charge above a grounded conducting plane at y=0. In this case you solve the problem using the method of images.
I have a slightly problem. Rather than having an infinitely thin conducting plane, mine occupies a region 0<y<a, i.e. it must now hold that V(x,y)=0 for 0<y<a.
Is it still possible to solve this using the image method?

2. Feb 2, 2016

### Dazed&Confused

For the area $y> a$ you can use the same image charge at the appropriate point below $y = a$. For the area $y < a$ you know can add an image charge $-q$ at the same spot as the original charge to cancel out the charge. Thus $V = 0$ at all the points $y \leq a$. This is a round about way of saying that the solution is to Laplace's equation is unique and since $V=0$ at the boundaries we know that $V=0$ is the unique solution for the entire area $y \leq a$.