>>11274131>>11273916this is a difficult type of problem because first you have to find the placing of the charges, which would be like Vespr but that seems non trivial for an arbitrary n.
Also, it's probably true that after a certain n, maybe n>4, you will not have a stable system.
Lets say you have n q- charges and one q+ charge. suppose largest distance between a q- and q+ charge is r, then the force on that q- charge will at the least push as much as (n-1)k(q/2r)^2-k(q/r)^2. this is because each other q- charge must be at the most 2r distance away by triangle inequality. when n=6, then this force will be positive and will always push away the farthest charge, making a unstable system.
I'm a math major so i actually had to look up the charge equation for two points - pretty pathetic!
