charges on a sphere; theorem?

From: elewars <elewars "at@at" trentu.ca>
Subject: charges on a sphere; theorem?
Date: Wed, 03 Oct 2001 13:35:52 -0400

2001 Oct 3
 Hello,
 A colleague pose this question.
 Suppose you have two like point charges (e.g. two protons, considered
 dimensionless), which must be on or inside a sphere. The minimum energy
 geometry (MEG) is that they be on the surface, at the ends of a diameter
 of the sphere. For three charges, the MEG is on the surface, at the
 corners of an equilateral triangle. And so on for 4, 5, ...? charges,
 the MEG having all of them on the surface.
 Question: is there a number or numbers _n_ of charges for which
 migration of one or more charges _into_ the sphere would lower the
 energy? Is there some theorem in math or physics that deals with this?
 Thanks
 E. Lewars
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