Repulsive force by itself on a charged sphere

[Zeor137]

I was wondering how could I hold a lot of charge inside, for example, a ball. I thought by wrapping it in an isolant and using a hole with a semiconductor to charge it without letting anything out. But them it also could blow apart by the repulsive force of itself. Therefore, I got curious of how to calculate the pressure necessary to hold it still. I thought about considering it a bunch of infinitesimal balls with infinitesimal charge but I don't now enough calculus yet to put it in a equation.

 

[UltrafastPED]

For any conducting sphere all of the extra charge will move to the surface; any other configuration is unstable.

The math is given here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html#c2

Your question then becomes: what are the mechanical stresses on the charged spherical shell with surface charge? This was investigated extensively around 1900 while trying to understand the properties of the newly discovered electron. For example, Poincare stress:
http://en.wikipedia.org/wiki/Electromagnetic_mass#4.2F3_problem