A self-consistent consideration of the Lienard-Wiechert solition is given including its heuristic deduction, which involves a future light cone (thus the lightlike propagation of information from an arbitrarily moving pointlike charge), and physical interpretation of this field via application of three distinct reference frames (of an inertial observer, then a non-inertial one retardedly co-moving with the charged source, and finally, co-moving with the electromagnetic field). In the last frame the magnetic part of the Lienard-Wiechert field identically (though not asymptotically) vanishes in all spacetime together with the Poynting vector. In the second frame, the properties of energy redistribution and radiation of the field are discussed. The dynamically caused propagation velocity of the Lienard-Wiechert electromagnetic field in a vacuum at any final distance from the source is less than that of light.
We present an elegant derivation of the Doppler factor in the Lienard-Wiechert potentials of an extended particle, based on a theorem authored by J. L. Synge and dealing with cross-sections through worldtubes.
Retarded electromagnetic potentials are derived from Maxwell's equations and the Lorenz condition. The difference found between these potentials and the conventional Liénard-Wiechert ones is explained by neglect, for the latter, of the motion-dependence of the effective charge density. The corresponding retarded fields of a point-like charge in arbitary motion are compared with those given by the formulae of Heaviside, Feynman, Jefimenko and other authors. The fields of an accelerated charge given by the Feynman are the same as those derived from the Liénard-Wiechert potentials but not those g…
We present an in depth analysis and a new derivation of the Doppler factor in the Lienard-Wiechert potentials, based on geometrical considerations in Minkowski space. We argue that, contrary to a common assumption, the methods used for deriving the Doppler factor in the case of an electrically charged extended particle are not applicable in the case of a point particle. A geometrical interpretation of the Doppler factor is nonetheless found in the later case, based on the electromagnetic interaction model of Fokker. In this model the interaction takes place between infinitesimal worldline segm…
Calculating the electromagnetic field of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. While the correct field has been obtained many times and through various means, it remains somewhat unclear why the (supposedly general) field expression derived from the Liénard-Wiechert potentials misses some terms. We present new derivations of the missing field and potential terms by considering only pure hyperbolic motion, and we amend the offending step in the standard Liénard-Wiechert construction.
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and Faraday's law remains unknown to this day. Furthermore, the Lorentz force is considered as experimental phenomena, the theoretical foundation of this force is still unknown. To answer these fundamental theoretical questions, we derive Lienard Wiechert potentials, Maxwell's equations and Lorentz force from two simple postulates: (a) when all charges are at rest the…
The aim of this paper is to investigate the fundamental problems of retardation and radiation caused by non-uniformly moving point sources using the theories of electrodynamics and elastodynamics. This paper investigates and compares the retarded electromagnetic fields and the retarded elastodynamic fields. For the non-uniform motion of a general point source, the Liénard-Wiechert type potentials and the radiation and nonradiation fields are derived for a point charge and for a point force.
The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Liénard-Wiechert potentials. The exact closed-form solutions of the displacement and elastic fields produced by the point force and line forces are calculated. The displacement fields can be identified with the elastodynamic Liénard-Wiechert tensor potentials. For a non-uniformly moving point force, we decompose the elastic fields into a radiation part and a non-radiation part. We…
The purpose of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space-dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key-formulae for the dynamics of dislocations are …
In connection with the discussion and the measurements fulfilled in [R. de Sangro et al., Eur. Phys. J. C 75 (2015) 137], the full identity is demonstrated between the Feynman formula for the field of a moving charge and the Lienard-Wiechert potentials.
In this paper, we investigate the so-called Bopp-Podolsky electrodynamics. The Bopp-Podolsky electrodynamics is a prototypical gradient field theory with weak nonlocality in space and time. The Bopp-Podolsky electrodynamics is a Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We derive the retarded Green functions, first derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strengths in the framework of the Bopp-Podolsky electrodyn…
In this work, the theory of second gradient electrodynamics, which is an important example of generalized electrodynamics, is proposed and investigated. Second gradient electrodynamics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian density. Second gradient electrodynamics possesses a weak nonlocality in space and time. In the framework of second gradient electrodynamics, the retarded Green functions, first-order derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, gen…
Maxwell's electrodynamics postulates the finite propagation speed of electromagnetic (EM) action and the notion of EM fields, but it only satisfies the requirement of the covariance in Minkowski metric (Lorentz invariance). Darwin's force law of moving charges, which originates from Maxwell's field theory complies the Lorentz invariance as well. Poincaré's principle stating that physical laws can be formulated with identical meaning on different geometries suggest, that the retarded EM interaction of moving charges might be covariant even in Euclidean geometry (Galilean invariance). Keeping th…
We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an action-at-a-distance behavior in Coulomb gauge. The conundrum generated by the instantaneous interaction has intrigued physicists for a long time. Starting from the differential equations that couple the sources to the potentials, we here show in a concise derivation, using the retarded Green function, how the instantaneous interaction cancels in the calculatio…
