Working within the framework of the classical theory of electrodynamics, we derive an exact mathematical solution to the problem of self-field (or radiation reaction) of an accelerated point-charge traveling in free space. We obtain relativistic expressions for the self-field as well as the rates of radiated energy and linear momentum without the need to renormalize the particle’s mass – or to discard undesirable infinities.

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Masud Mansuripur, "Self-field, radiated energy, and radiated linear momentum of an accelerated point charge," Proc. SPIE 10732, Spintronics XI, 1073230 (Presented at SPIE Nanoscience + Engineering: August 23, 2018; Published: 20 September 2018); https://doi.org/10.1117/12.2322082.