Double (implicit and explicit) dependence of the electromagnetic field of an accelerated charge on time: Mathematical and physical analysis of the problem

Abstract

We considered the electromagnetic field of a charge moving with a constant acceleration along an axis. We found that this field obtained from the Liénard-Wiechert potentials does not satisfy Maxwell equations if one considers exclusively a retarded interaction (i.e. pure implicit dependence this field on time). We show that if and only if one takes into account both retarded interaction and direct interaction (so called "action-at-a-distance") the field produced by an accelerated charge satisfies Maxwell equations.

ReVTeX file, no figures, 12pp

References in corpus (3)

• Convection displacement current and alternative form of Maxwell-Lorentz equations
• Coulomb field of an accelerated charge: physical and mathematical aspects
• On the Physical Origin of the Oppenheimer-Ahluwalia Zero-Energy Solutions

Cited by in corpus (6)

• Instantaneous fields in classical electrodynamics
• Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics
• Criticism of "Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics" by Andrew E. Chubykalo and Stoyan J. Vlaev
• Comment on 'Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics,' by Chubykalo et al [Found. of Phys. Lett, 19, 37-46 (2006)]
• On momentum and energy of a non-radiating electromagnetic field
• About the Simultaneous Co-Existence of Instantaneous and Retarded Interactions in Classical Electrodynamics