Savchenko Problem 7.4.8
Physics · mechanics
Problem
Two electrons are located at a distance r from each other, and the velocity of one of them is zero, and the velocity of the other is directed at an acute angle to the line connecting the electrons. What will be the angle between the electron velocities when they are again at a distance r from each other?Intuitive explanation
The key insight is that the electrons' separation distance returns to due to the symmetry of their Coulomb interaction and conservation laws. Since the repulsive force acts along the line joining them, momentum is conserved in the direction perpendicular to this line, while the radial component changes. When the separation returns to , the geometry of the trajectory—combined with energy and momentum conservation—forces the velocity vectors into a specific configuration. The angle you're looking for emerges from the constraint that both the distance and the initial conditions are symmetric.
Intuitive explanation
The key insight is that the electrons' separation distance returns to due to the symmetry of their Coulomb interaction and conservation laws. Since the repulsive force acts along the line joining them, momentum is conserved in the direction perpendicular to this line, while the radial component changes. When the separation returns to , the geometry of the trajectory—combined with energy and momentum conservation—forces the velocity vectors into a specific configuration. The angle you're looking for emerges from the constraint that both the distance and the initial conditions are symmetric.