I am designing a 2d game in which a \$1/r^2\$ force acts between moving charged particles, and the number \$n\$ of particles is very large. To calculate the force between all pairs of particles is about \$n^2/2^2\$.
How well does this scale in practice when there are hundreds or thousands or particles? (And considering that graphical output is simple, so that we want to compute the positions of all particles ~60 times per second.)
If scaling is bad, how can I simplify the game design such that – in practice – it's not an issue any more? (For example, I have thought of constraining all particles to a lattice of discrete sites, but then I don't know how movement in arbitrary directions would work).