We know from Chapter 2 that the potential energy of two point charges q ₁ and q ₂ separated by a distance r is q ₁ q ₂/ r. This is a mutual potential energy that belongs to both of these point charges jointly. This potential energy equals the work that we must do on the charges to bring them to a distance r from one another, starting at infinite distance. In the present a chapter, we will develop a general expression for the potential energy of an arbitrary system of many point charges, and we will discover that this potential energy can be expressed as an integral of an energy density which is proportional to E ².

In the interpretation of the electric potential energy, we are faced with a question: Is the potential energy located at the point charges or is it located in the electric fields? This question has no answer in the context of electrostatics, because the outcome of experiments in electrostatics is independent of where the energy is located. In principle, we could decide this question with a gravitational experiment all forms of energy exert gravitational attractions, and if the electrostatic energy is distributed over the electric field, then the electric field should exert gravitational attractions. Unfortunately, these gravitational effects are so small that a direct measurement is impossible. To decide where the electric energy is located, we must go beyond electrostatics. We must look at electromagnetic...