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## Main Question or Discussion Point

First by "stationary" I mean "with respect to each other" so as to avoid introducing relativity problems.

I'm wondering whether there's a way to prove or disprove that given [itex]N > 1[/itex] point charges [itex]q_1, q_2, ..., q_n[/itex], is there always a way of putting them in 3-dimensional space such that all of them remain stationary after release. Assume that when putting a new single point charge to the desired position I use mechanical force to fix the old ones at where they are.

What I've tried:

For [itex]N = 1[/itex] obviously I can do this but for [itex]N = 2[/itex] I can't. I first came up with the idea to investigate the case of [itex]N[/itex] charges based on the case of [itex]N-k \, (0 < k < N)[/itex] charges. However I didn't think of anything valuable in this way, it's not clear to me how the equilibrium of [itex]N-k[/itex] charges could be related to the equilibrium of [itex]N[/itex] charges.

Any help will be appreciated :)

I'm wondering whether there's a way to prove or disprove that given [itex]N > 1[/itex] point charges [itex]q_1, q_2, ..., q_n[/itex], is there always a way of putting them in 3-dimensional space such that all of them remain stationary after release. Assume that when putting a new single point charge to the desired position I use mechanical force to fix the old ones at where they are.

What I've tried:

For [itex]N = 1[/itex] obviously I can do this but for [itex]N = 2[/itex] I can't. I first came up with the idea to investigate the case of [itex]N[/itex] charges based on the case of [itex]N-k \, (0 < k < N)[/itex] charges. However I didn't think of anything valuable in this way, it's not clear to me how the equilibrium of [itex]N-k[/itex] charges could be related to the equilibrium of [itex]N[/itex] charges.

Any help will be appreciated :)