Electromagnetic inertia, reactive energy and energy flow velocity

Abstract

In a recent paper titled Coherent electromagnetic wavelets and their twisting null congruences, I defined the local inertia density I(x, t), reactive energy density R(x, t), and energy flow velocity v(x, t) of an electromagnetic field. These are the field equivalents of the mass, rest energy, and velocity of a relativistic particle. Thus R = Ic2 is Lorentz-invariant and |v | ≤ c, with equality if and only if R = 0. The excep-tional fields with |v | = c were called coherent because their energy moves in complete harmony with the field, leaving no inertia or re-active energy behind. Generic electromagnetic fields become coherent only in the far zone. Elsewhere, their energy flows at speeds v(x, t) < c, a statement that is surprising even to some experts. 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 elec-tric 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 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. 1 ar