Electromagnetic Fields of Accelerated Nonradiating Charge Distributions

Abstract

Exact expressions for the retarded electromagnetic potentials are derived for certain extended, rigid, accelerated, but nonradiating charge-current distributions. An unexpected result is that the oscillating parts of these potentials vanish identically for all points of space-time which are outside the distributions. Since each of these nonradiating distributions undergoes time-periodic orbital motion, with the "radius" of the orbit less than the radius of the distribution, this result means that the oscillating part of the electromagnetic field energy is localized within a volume of the same order as the volume of the distribution.