The nature of electromagnetic energy

Abstract

The nature of the electromagnetic (EM) energy for general charge and current distributions is analyzed. There are two well known forms for calculating EM energy as the integral over all space of either the electromagnetic fields: u_{\bf EB}=({\bf E\bcdot D+B\bcdot H})/8\pi, or the electromagnetic potentials and charge-current densities: u_{\rho{\bf A}}=1/2(\rho\phi+{\bf j\bcdot A}). We discuss the appropriate use of each of these forms in calculating the total EM energy and the EM energy within a limited volume. We conclude that only the form $u_{\bf EB}$ can be considered as a suitable EM energy density, while either form can be integrated to find the total EM energy. However, bounding surface integrals (if they don't vanish) must be included when using the $u_{\bf EB}$ form. Including these surface integrals resolves some seeming paradoxes in the energy of electric or magnetic dipoles in uniform fieldsComment: The discussion and conclusions have been modifie