Electromagnetic inertia, reactive energy, and energy flow velocity

TL;DR

This paper investigates the local energy flow velocity, inertia, and reactive energy in electromagnetic fields, confirming that only far-zone fields are fully coherent with energy moving at the speed of light.

Contribution

It clarifies how electromagnetic energy flow varies locally in different field configurations and confirms that coherence with energy moving at light speed occurs only in the far zone.

Findings

Reactive energy remains near sources in near fields.

Energy can flow inward and transversally in time-dependent dipole fields.

Time-averaged velocities do not reveal local energy flow complexities.

Abstract

In a recent paper titled "Coherent electromagnetic wavelets and their twisting null congruences," I defined the local inertia density (I), reactive energy density (R), and energy flow velocity (v) of an electromagnetic field. These are the field equivalents of the mass, rest energy, and velocity of a relativistic particle. Thus R and I are Lorentz-invariant and |v|<=c, with equality if and only if R=0. The exceptional fields with |v|=c were called "coherent" because their energy moves in complete harmony with the field, leaving no inertia or reactive energy behind. Generic electromagnetic fields become coherent only in the far zone. Elsewhere, their energy flows at speeds |v|<c. The purpose of this paper is to confirm and clarify this statement by studying the local energy flow in several common systems: a time-harmonic electric dipole field, a time-dependent electric dipole field, and a standing plane wave. For these fields, the energy current (Poynting vector) is too weak to carry away all of the energy, thus leaving reactive energy in its wake. For the time-dependent dipole field, we find that the energy can flow both transversally and inwards, back to the source. Neither of these phenomena show up in the usual computation of the energy transport velocity which considers only averages over one period in the time-harmonic case.