Electric Potential Energy

The definition of the electric potential energy of a system of charges is the work required to bring them from infinity to that configuration.

To workout the electric potential energy for a system of charges, assume a charge q₂ at infinity and at rest as shown in figure 1.1. If q₂ is moved from infinity to a distance r from another charge q₁, then the work required is given by

Substitute for V in the equation of work

To calculate the potential energy for systems containing more than two charges we compute the potential energy for every pair of charges separately and to add the results algebraically.

If the total electric potential energy of a system of charges is positive this correspond to a repulsive electric forces, but if the total electric potential energy is negative this correspond to attractive electric forces.