On the Foundations of the Classical Relativistic Theory of the Field of an Accelerated Extended Charge

Abstract

The effect of nonzero extent of an electric charge is considered within the assumption that the structure of the charge at rest is spherically-symmetric and the current vector is linear in the acceleration. An exact expression for the electromagnetic field of the charge is obtained, which depends on the specific form of the charge distribution. We have developed the approximations which deal with the charge distribution through its low-order moments, for the case in which the particle velocity does not considerably change over the time it covers a distance of the order of its own size. We have also rigorously justified the Lorentz-Abraham-Dirac expression for the radiation friction (we have identified a more general context for this expression as well as its applicability domain). We have also studied the radiation field and demonstrated that in some cases, the radiation virtually vanishes even for large accelerations. Ways of further development of the theory have been pointed out, in order to include more general forms of the current vector (dependence of the deformation of the charge structure on the acceleration, rotation of the structure around the centre of the charge, ultrarelativistic regimes).