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 Stevens Aug 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.