Electric potential energy
Also called U_E
Electric potential energy is the energy a configuration of charges holds because of where the charges sit, measured in joules. For two point charges it is the Coulomb constant times the product of the signed charges divided by their separation, with zero taken at infinity.
Electric potential energy belongs to a configuration, not to a lone charge. For two point charges it is the work an external force must do to bring them from infinitely far apart to their present separation:
Three details carry most of the marks.
- The signs go in. No absolute value bars, unlike Coulomb's law. Like charges give , because work was done against their repulsion. Opposite charges give , a bound pair you would have to supply energy to separate.
- appears to the first power. Squaring it imports the exponent from the force law, where it does belong.
- More than two charges means summing over pairs. Each distinct pair contributes one term.
Joules, not volts. The units are what keep the two quantities apart. Electric potential is energy per coulomb and describes a location; electric potential energy is the energy itself and depends on which charge you put at that location. The bridge is , printed on the sheet: a potential difference in volts times a charge in coulombs gives an energy in joules.
That bridge carries the sign too. A positive charge moving to lower potential loses potential energy, while a negative charge moving to lower potential gains it, because is negative in the same equation.