Why charges go to the surface: A generalized Thomson problem

@article{Levin2003WhyCG,
  title={Why charges go to the surface: A generalized Thomson problem},
  author={Yan Levin and Jeferson J. Arenzon},
  journal={EPL},
  year={2003},
  volume={63},
  pages={415-418}
}
We study a variant of the generalized Thomson problem in which n particles are confined to a neutral sphere and interacting by a 1/rγ potential. It is found that for γ ≤ 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However, for γ > 1 and n > nc(γ) 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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