# Green's Function Using Image Charge

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1. Oct 23, 2014

1. The problem statement, all variables and given/known data
Write an expression for the Dirichlet Green's function of the part of the space bounded by two infinite conducting plates parallel each other and separated by distance of d. Use Image charge method

2. Relevant equations
G (at z=0) =0, G (at z=d) =0
I guess
3. The attempt at a solution
I am confuse about image charge method. What is the actual principles of this method?
On most of problem I ever seen, when we use image method, there is always a point charge in the system, however in this case not. Can anyone help me?

2. Oct 23, 2014

### moriheru

Is this a QM greensfunction, such as the ones used in perturbation thoery, or a classical?

3. Oct 23, 2014

It is classical

4. Oct 23, 2014

### moriheru

Ah yes just saw, can't help you sorry. I know QM but my classical physics is a bit rusty.

5. Oct 23, 2014

### RUber

I have not done this problem before, but if you are building the green's function for one infinite plate, it is the limit as the point charge approaches the plate + its image being reflected back at it. It seems like for 2 plates, you will have to satisfy the 2 boundary conditions. Here is what appears to be a good explanation of the single plate case (and other examples).
http://www.phys.lsu.edu/~jarrell/COURSES/ELECTRODYNAMICS/Chap2/chap2.pdf

6. Oct 24, 2014

### vela

Staff Emeritus
The Green's function is essentially the potential due to a point charge. The potential will be a function of $\vec{r}$, the position of the point charge.