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Two particles X and Y have equal mass but different positive charges and are free to move. Initially they are far apart with Y at rest, and X moves toward Y with initial speed u. After a very long time, what happens?

1. X will stop, Y will move with velocity u.
2. X and Y will both move with velocities u/2 each.
3. X will stop, Y will move with velocity < u.
4. both will move with velocities < u/2.

Correct answer: X will stop, Y will move with velocity u.

Solution

The Coulomb interaction is conservative, so the encounter is like a 1-D elastic 'collision' between equal masses. For equal masses in an elastic head-on collision, the velocities are exchanged: the incoming particle (X) stops and the target (Y) moves off with speed u. Momentum (m*u) and kinetic energy (1/2 m u²) are both conserved at the final far-apart state.

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