Working within the framework of the classical theory of electrodynamics, we derive an exact mathematical solution to the problem of self-force (or radiation reaction) of an accelerated point-charge traveling in free space. In addition to deriving relativistic expressions for self electromagnetic fields, we obtain exact formulas for the rates of radiated energy and linear momentum without the need to renormalize the particle’s mass – or to discard undesirable infinities. The relativistic expression of self-force known as the Abraham- Lorentz-Dirac equation is derived in two different ways. Certain properties of the self-force are examined, and an approximate formula for the self-force, first proposed by Landau and Lifshitz, is discussed in some detail.
Masud Mansuripur, "Self-field, radiated energy, and radiated linear momentum of an accelerated point charge: part 2," Proc. SPIE 10926, Quantum Sensing and Nano Electronics and Photonics XVI, 109260O (Presented at SPIE OPTO: February 04, 2019; Published: 1 February 2019); https://doi.org/10.1117/12.2511214.
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