The nature of electromagnetic energy

TL;DR

This paper examines the distribution and localization of electromagnetic energy in radiation and static charge cases, clarifying where energy resides and challenging the notion of energy density in static fields.

Contribution

It provides a clear analysis distinguishing energy localization in electromagnetic radiation and static charges, emphasizing the actual energy containment regions.

Findings

Electromagnetic radiation's energy density is  ext{pi}}(E^2+B^2).

Static charge energy is contained within the charge, not in the fields.

No ambiguity exists about the energy location in either case.

Abstract

We study the nature and location of electromagetic energy for two cases. The energy density for electromagnetic radiation is shown to be $\frac{1}{8\pi}(E^2+B^2)$, with the energy contained in the electromagnet fields. For a static charge distribution, the electromagnet energy is contained in the charge, with an energy density, $\frac{1}{2}\rho\phi$, There is no energy outside the charge distribution. The electromagnetic fields do not contain the energy, and $\frac{1}{8\pi}(E^2+B^2)$ cannot be considered an energy density in this case. There is no ambiguity in either case as to where the energy is located.