electric potential energy

Electric potential energy is the stored energy in a set of charges due to their positions, just as a lifted rock stores gravitational potential energy due to its height. Push two like charges together against their repulsion and you store energy in them, like compressing a spring; let them go and that energy is released as they fly apart.

For two point charges q1 and q2 separated by a distance r, the electric potential energy is U = k q1 q2 / r, with k the Coulomb constant and U measured in joules (J). The sign carries meaning: for like charges (both positive or both negative) U is positive and grows as they get closer, since you must do work to push them together. For opposite charges U is negative, meaning energy would have to be supplied to pull them apart. The zero of U is chosen at infinite separation.

Potential energy matters because the electric force is conservative, so energy converts cleanly between potential and kinetic forms. As a proton flies away from another proton, its potential energy drops and its kinetic energy rises by the same amount, keeping the total constant. This bookkeeping powers everything from the electron volt used in atomic physics to the energy stored in a charged capacitor.