Electrostatic Potential Energy of Two Point Charges and of a Dipole in an Electrostatic Field

The idea of potential energy from section 8.3, for just two charges, generalises directly to any number of charges by thinking OPERATIONALLY about how a system of charges is physically ASSEMBLED: imagine bringing every one of the charges, one at a time, from an initial state where they are all infinitely far apart (and hence, by convention, have zero mutual potential energy) to their actual final positions. While the charges are still infinitely separated there is no field to work against, so no work at all is needed for that starting state.

As each subsequent charge is brought in from infinity, however, it must be moved through the combined field of every charge already in place -- and if the charges being brought together are of LIKE sign, work must be done AGAINST their mutual repulsion at every step. Because the electrostatic force is conservative (section 8.3), all of this assembly work is stored, without loss, as the final configuration's electrostatic potential energy -- fully recoverable later if the charges are released and allowed to fly apart again under their own mutual repulsion. …