I was just curious actually.
Is it possible to release a set of point-sized charges in space, each particle at rest, such that after a period of time, the system returns to its initial configuration of positions. The particles can have unequal masses and charges.
(Newton's laws and Coulumb's law apply, relativity doesn't. Induction of charge does not occur, charges cannot touch each other in a valid example)
It looked easy at first, but I couldn't find any example of the same. Can the statement be disproved, maybe using Gauss law and unstable equilibrium?
P.S. If it is possible, what is the minimum number of charges required to achieve this?
P.S.2 @rpfphysics has noted that the question is trivial if we allow charges to pass through each other. Hence I'm asking for examples where they do not.