Why charges go to the surface: a generalized Thomson problem
Abstract
We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/rg potential. It is found that for g 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>nc(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes.
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