Summary: Europhys. Lett., 63 (3), pp. 415418 (2003)
EUROPHYSICS LETTERS 1 August 2003
Why charges go to the surface:
A generalized Thomson problem
) and J. J. Arenzon(
Instituto de F´isica, Universidade Federal do Rio Grande do Sul
Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
(received 28 April 2003; accepted in final form 5 June 2003)
PACS. 71.10.Ca Electron gas, Fermi gas.
PACS. 64.60.Cn Order-disorder transformations; statistical mechanics of model systems.
Abstract. We study a variant of the generalized Thomson problem in which n particles are
confined to a neutral sphere and interacting by a 1/r
potential. It is found that for 1 the
electrostatic repulsion expels all the charges to the surface of the sphere. However, for > 1
and n > nc() 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.
In a recent paper , Bowick et al. studied a system of particles confined to the surface of
a sphere and interacting by a repulsive 1/r