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/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(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.

References in corpus (5)

• Electrostatic correlations: from Plasma to Biology
• Grain Boundary Scars and Spherical Crystallography
• Screening of a macroion by multivalent ions: Correlation induced inversion of charge
• Crystalline Order on a Sphere and the Generalized Thomson Problem
• Strong electrostatic interactions in spherical colloidal systems

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• Tunable Order of Helically Confined Charges
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• The Effect of Charge Discretization on the Electrical Field inside a Conductor
• Some spherical codes in S2 and their algebraic numbers