Implications of a non-zero Poynting flux at infinity sans radiation reaction for a uniformly accelerated charge

Abstract

We study in detail the electromagnetic fields and the Poynting flux in the case of a uniformly accelerated charge, in order to examine whether such a charge does `emit' radiation, especially in view of the widely accepted fact that there is no radiation reaction on the charge. Our concern, in particular, is with the Poynting flow computed at large distances (approaching infinity!) from the time-retarded positions of uniformly accelerated charge, and taken as an evidence of radiation emitted by the charge, which we shall demonstrate to be not true. As the charge picks up speed due to a constant acceleration, the energy in its self-fields accordingly increases and the Poynting flow, usually inferred as radiation, actually forms part of the requisite energy being fed into fields, at a rate just sufficient to match the increasing energy in its self-fields at various distances from the uniformly accelerated charge, including that in the far-off regions. In fact, for the decelerating charge, the energy in its self-fields decreases, at all distances from the charge, till it comes to momentary rest with no energy in its transverse fields, and this decrease in energy is shown {\em everywhere} by an inward radial flow of the Poynting vector, toward the `present' position of the decelerating charge. Moreover, there is a convective flow of self-fields of the charge, seen as a Poynting flow component always along the `present' direction of motion of the charge. Further, we shall show that effectively the electromagnetic fields, including the acceleration fields, even when they are at large distances from the time-retarded position of the charge, they continue to be all around the `present' position of the charge which itself is moving toward infinity due to the uniform acceleration.