On the Interaction of Extended Charges in Classical Relativistic Theory

Magomed B Ependiev

doi:10.4236/jmp.2017.84044

Abstract

Basic set of equations of motion for particles in the case when charge distribution of a particle at rest is spherically symmetric and localized is formulated. Various approximations for interaction forces are derived. The basic approximation is justified by the fact that particle velocities vary little on a time scale σ0/c ( σ0~localization radius). Examples of large and small (with respect to σ0) distances between particles are considered. In both cases the slow motion approximation is derived. Apart from calculation of the corrections to the point charge interaction at large distances an approach to the analysis of neutral particles (missing in the point particle theory) containing charged fragments is proposed. In addition, it is shown that at small distances charges of the same sign may attract if their mechanical masses are substantially small.

Highlights

Classical electrodynamics is intrinsically inconsistent at distances of the order of or less than the “radius” of the electron (see (37.3) in [1])
In [5] the author considered this problem in general setup having investigated properties of the field created by an accelerated extended charged particle
First of all it is clear that improving the theory to a better perfection is useful from mathematical stand point

Summary

Introduction

Classical electrodynamics is intrinsically inconsistent at distances of the order of or less than the “radius” of the electron (see (37.3) in [1]). 1) Currently a combination of relativism along with large acceleration of extended charges can be only observed at microscopic level that is governed by quantum theory It does not exclude similar phenomena where classical electrodynamics still applies. The original system of equations of motion for the extended charge dynamics results from setting the variation of the action to zero while varying particle trajectories (i.e. it is assumed that the field produced by charges is unambiguously defined by their trajectories). This system is relatively simple in its form though hardly applicable in practice making the derivation of the “working” approximations extremely cumbersome. To put it clear and short we provide our work with the notations, our analysis scheme and concluding appendix that contains all cumbersome expressions

Notation and Analysis Scheme

Basic System of Equations

Limited Accelerations

Large Distances

Small Distances

Conclusion