# Charge Distribution on Two Neighboring Conductors

1. Dec 5, 2011

### conquerer7

Say you have two spherical conductors, of radius r, centers a distance d apart. Both have charges of +Q. What are the charge distributions on them?

My physics book more or less handwaves and says it'll be more or less unaffected, but is there a way to solve this exactly?

2. Dec 6, 2011

### Naty1

I haven't solved an problems like that in many,many years...but I can provide a bit of an insight:

are these solid or hollow conductors.....?

anyway, Say d is much, much greater than r....there should be a uniform distribution on each sphere...now bring them close together, say d is just a bit bigger than 2 r so they are close.....like charges will repel somewhat at the closest point, less so further...so it sure
seems like the charge distribution WILL change....I disagree it would be "unaffected".

3. Dec 6, 2011

### Meir Achuz

This problem can be solved with a sequence of image charges. It gets quite complicated, but for d>>a, the series converges fast.