Two point charges in the vacuum (so ignore all frictions). They have opposite signs so they will move towards each other under Coulomb's force. The magnitude of their charges are $q_1$ and $q_2$ respectively, their distance is $l$, and their masses are $a$ and $b$. They start from a static location before they start traveling towards each other.
How long does it take before they collide?
I guess one can set up an differential equation for this. We set an equation for conservation of energy, where electric potential is being converted into kinetic energy, and another equation for conservation of momentum, based on the distance two charges have traveled. But the computation is tedious.. Is there an easier solution? It looks like a classical setup that should come with a more elegant solution though.. .
[EDIT] I wonder if Kepler's Third Law works since it assumes the force between two entities are proportional to the masses, but not the case here.
