Savchenko Problem 7.4.5

This is a collision problem governed by conservation of energy and momentum—two electrons repel via Coulomb force, so they'll never actually collide, but reach a closest approach where all their kinetic energy converts to electric potential energy. The key insight is that in the center-of-mass frame, the problem becomes symmetric: both electrons decelerate equally until they momentarily stop, then bounce apart. Use conservation of momentum to find the CM velocity, then energy conservation in that frame to find when kinetic energy equals the electrostatic potential energy $U = \frac{ke^2}{r}$.

This is a collision problem governed by conservation of energy and momentum—two electrons repel via Coulomb force, so they'll never actually collide, but reach a closest approach where all their kinetic energy converts to electric potential energy. The key insight is that in the center-of-mass frame, the problem becomes symmetric: both electrons decelerate equally until they momentarily stop, then bounce apart. Use conservation of momentum to find the CM velocity, then energy conservation in that frame to find when kinetic energy equals the electrostatic potential energy $U = \frac{ke^2}{r}$.