Working Paper Article Version 1 This version is not peer-reviewed

Discrepancy between Power Radiated and the Power Loss Due to Radiation Reaction for an Accelerated Charge

Version 1 : Received: 13 September 2020 / Approved: 13 September 2020 / Online: 13 September 2020 (15:41:40 CEST)

How to cite: Singal, A.K. Discrepancy between Power Radiated and the Power Loss Due to Radiation Reaction for an Accelerated Charge. Preprints 2020, 2020090292 Singal, A.K. Discrepancy between Power Radiated and the Power Loss Due to Radiation Reaction for an Accelerated Charge. Preprints 2020, 2020090292

Abstract

We examine here the discrepancy between the radiated power, calculated from the Poynting flux at infinity, and the power loss due to radiation reaction for an accelerated charge. It is emphasized that one needs to maintain a clear distinction between the electromagnetic power received by a set of far-off observers and the instantaneous mechanical power loss of the charge. In literature both quantities are treated as not only equal but almost synonymous, however, the two, in general, need not be so. It is shown that in the case of a periodic motion, the two formulations do yield the same result for the power loss in a time averaged sense, though, the instantaneous rates could be quite different. It is demonstrated that the difference in the two power formulas is nothing but the difference in the rate of change of energy in self-fields of the charge between the retarded and present times. In particular, in the case of a uniformly accelerated charge, power going into the self-fields at the present time is equal to the power that was going into the self-fields at the retarded time plus the power going in acceleration fields, usually called radiation. From a comparison of far fields with the instantaneous position of the uniformly accelerated charge, it is shown that all its fields, including the acceleration fields, remain around the charge and are not radiated away from it.

Subject Areas

Classical electromagnetism; Applied classical electromagnetism. Radiation by moving charges; radiation or classical fields

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