Electric Field Between Two Metal Balls.

[tade]

Imagine you have two identical metal balls, each carrying the same amount of charge, but with one ball being positive and the other negative.

When you bring them close together, there will be polarization, so you can no longer treat the balls as point charges.

How does one find the charge distribution/electric field/potential of the balls?

 

[tade]

I can formulate an integral equation based on the condition for electrostatic equilibrium, but that equation is pretty hard to solve.

This problem has definitely been addressed before, but Google is not helping me much, if any of you know of a solution please post the link.