Instantaneous fields in classical electrodynamics

Abstract

In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function whose spatial and temporal derivatives transform the instantaneous fields into the retarded ones. We conclude that the instantaneous fields can formally be introduced as unphysical objects into classical electrodynamics which can be used to find the physical retarded fields.

A minor correction is made in the abstract of the version published in Europhys. Letts

References in corpus (5)

• From Lorenz to Coulomb and other explicit gauge transformations
• Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method
• Double (implicit and explicit) dependence of the electromagnetic field of an accelerated charge on time: Mathematical and physical analysis of the problem
• Criticism of "Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics" by Andrew E. Chubykalo and Stoyan J. Vlaev
• About the Simultaneous Co-Existence of Instantaneous and Retarded Interactions in Classical Electrodynamics

Cited by in corpus (14)

• Can Maxwell's equations be obtained from the continuity equation?
• A formal interpretation of the displacement current and the instantaneous formulation of Maxwell's equations
• How potentials in different gauges yield the same retarded electric and magnetic fields
• The Galilean limits of Maxwell's equations
• Preacceleration without radiation: the non-existence of preradiation phenomenon
• The Kirchhoff gauge
• Comment on 'A generalized Helmholtz theorem for time-varying vector fields by A. M. Davis, [Am. J. Phys. 74, 72-76 (2006)]'
• On Feynman's handwritten notes on electromagnetism and the idea of introducing potentials before fields
• The exact Darwin Lagrangian
• 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)]
• A short proof that the Coulomb-gauge potentials yield the retarded fields
• An axiomatic approach to Maxwell's equations
• The Coulomb static gauge
• Reply to "Comment on `Can Maxwell's equations be obtained from the continuity equation?'" by E. Kapuscik [Am. J. Phys. 77, 754 (2009)]