(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\Omega = \left{ \left( x,y,z \right) :,0<z<1 \right} [/tex]

Need to find Green's function using the method of images.

2. Relevant equations

none

3. The attempt at a solution

I can see that I will need an infinite sequence of images at each plane z = k, k = 0, +/- 1, +/- 2,... to make the potential on each boundary equal to zero.

let the positive charges be

[tex]r^{+}_{k} = (x,y,2k+z) \ and\ r^{-}_{k} = (x,y,2k-z) [/tex]

and Green's Function will look like

[tex] G(r',r) = \frac{1}{4\pi}\sum^{\infty}_{k = -\infty} \left[ \frac{1}{\left|r'-r^{+}_{k} \right| } - \frac{1}{\left|r - r^{-}_{k} \left| } \left] \left}[/tex]

How do I show that G(r',r) = 0 on the boundaries?

I also need to show that the sequences are convergent, and I haven't done that in so long I can't remember how.

Any suggestions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Green's Function using method of images

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**