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The Larmor formula giving radiation by a single point charge, is based on the Poynting’s theorem. It was argued in the earlier two articles*, that the Poynting’s theorem is suitable to get radiation by a continuous charge distribution and not a point charge. However, some authors have proved the Larmor formula without resorting to the Poynting’s theorem. This article scrutinises mathematics of one such method. All such methods essentially try to calculate work done by the field created by a point charge, on itself. We examine the related aspects in detail and realize that the Maxwell equations are suitable for calculating fields in the outside space and not for calculating self-fields on the point charge. Hence, any attempt to calculate the work done by the self-force will be incorrect. There seems to be no theoretical justification to suggest that an accelerating point charge should necessarily radiate.
1. A relook at radiation by a point charge. I (May 2017, Canadian Journal of Physics.)
Preprint: https://tspace.library.utoronto.ca/handle/1807/78885 ;
2. A relook at radiation by a point charge. II (May 2017, Canadian Journal of Physics.)