Classical formulations of the electromagnetic self-force of extended charged bodies

Abstract

Several noncovariant formulations of the electromagnetic self-force of extended charged bodies, as have been developed in the context of classical models of charged particles, are compared. The mathematical equivalence of the various dissimilar self-force expressions is demonstrated explicitly by deriving these expressions directly from one another. The applicability of the self-force formulations and their significance in the wider context of classical charged particle models are discussed.

Interpretations and Naturalness in the Radiation-Reaction Problem

“…In fact, when analysing physical situations that involve accelerations, one typically imposes that the acceleration regime is preceded by a state of inertial motion. All calculations we know of regarding extended charges explicitly or implicitly assume that the structure of the body is strictly rigid and that its charge is distributed with strict uniformity assuming some shape (e.g., a rigid and uniformly charged sphere; see, e.g., [64][65][66][67]; in the latter the author reviewed several rigid models comparing different approaches to the calculation of their behaviour). In special relativity a rigidity assumption is consistent with arbitrary rectilinear motion [65] (not with rotational motion).…”

Interpretations and naturalness in the radiation-reaction problem

“…All the calculations we know of regarding extended charges explicitly or implicitly assume that the structure of the body is strictly rigid and that its charge is distributed with strict uniformity assuming some shape (e.g. a rigid and uniformly charged sphere; see for instance [57,58]; in the latter the author reviews several rigid models comparing different approaches to the calculation of their behaviour). Rigidity is consistent with a regime of inertial motion and also with a regime of strict uniform proper acceleration throughout the body.…”

Electromagnetic Self-Force Mechanisms and Origin of <i>R</i><sup>-1</sup> Term

“…For an accessible calculation of simple cases of self-force, refer to [9] [10], for a more rigorous and general case [6] and for a comparison of different calculating methods [11]. Here we just report the results for a particle modeled as spherical shell of radius R .…”

“…r r E r r (11) In which r the source point and r is the field point. Note that in this integral the magnetic field is the source and due to the symmetry of the system only the ẑ component of it survives.…”