Electric Field Energy and Potential Energy

While electric field energy is the same as potential energy in some special cases, in general they are two different concepts. Field energy stands for the energy caused by the existence of the electric field such as the electric field in the electromagnetic waves; it doesn’t require the existence of the charges. Potential energy stands for the energy needed to assemble the charge system. It’s not a surprise to see the difference between these two concepts in a simple system composed of a positive charge q₁ and a negative charge q₂. Its field energy is positive while the potential energy is negative. The apparent conflict has been explained by Jackson by showing that if the self energy is excluded from the field energy, the field energy is the same as the potential energy. We show in this paper that the self energy needs to be considered only in a system of discrete point charges. The self energy needs not to be considered in the systems of charges on spherical shells, cylinders, and parallel sheets, where field energy is the same as the potential energy.