# How can we find the charge distribution of $n$ external electrons on the surface of a conducting cube? [closed]

Suppose we take 'n' electrons and put them on the surface of a conducting cube. How can we calculate the charge distrubution and position of these electrons once the static situation has been arrived at.

## closed as off-topic by M. Enns, Jon Custer, ZeroTheHero, Kyle Kanos, Aaron StevensAug 12 at 16:07

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The same problem on a sphere is called the Thomson problem and is unsolved (analytically, at least) for arbitrary $$n$$. I am virtually certain that the cubical version is as well.
The solution for $$n=2$$ is obvious. The solution for $$n=8$$ seems obvious but is probably nontrivial to prove.
• It can be answered with classical physics. It’s just electrostatics, but some electrostatics problems can only be solved numerically, on a computer, rather than analytically. You want to minimize the electrostatic potential, which is a function of $3n$ variables, so it is a high-dimensional minimization problem. – G. Smith Aug 12 at 15:40