scholarly journals NECESSITY OF SIMULTANEOUS CO-EXISTENCE OF INSTANTANEOUS AND RETARDED INTERACTIONS IN CLASSICAL ELECTRODYNAMICS

1999 ◽  
Vol 14 (24) ◽  
pp. 3789-3798 ◽  
Author(s):  
ANDREW E. CHUBYKALO ◽  
STOYAN J. VLAEV
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Direct Interaction ◽  
Classical Electrodynamics ◽  
Constant Acceleration ◽  
Action At A Distance ◽  
A Charge ◽  
Accelerated Charge

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

scholarly journals Classical electrodynamics and gauge symmetry of the X-boson

2018 ◽  
Vol 33 (25) ◽  
pp. 1850148
Author(s):  
Mario J. Neves ◽  
Lucas Labre ◽  
L. S. Miranda ◽  
Everton M. C. Abreu
Keyword(s):  
Gauge Symmetry ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Massless Particle ◽  
Space Time ◽  
Dispersion Relations ◽  
Classical Electrodynamics ◽  
Gauge Transformations ◽  
Boson Model ◽  
A Charge

The classical electrodynamics for X-boson model is studied to understand it propagation in the space–time. The Maxwell equations of model and the correspondents wave equations are obtained. It indicate the dispersion relations of a massive and massless particle, that we interpret as photon and the X-boson. Thereby, a full diagonalization of the model is introduced to get a Maxwell sector summed up to Proca sector. Posteriorly, the X-fields and X-potentials of a relativistically moving charge is obtained in terms of a time-proper integral, and as an example, we calculate the fields and potentials for a charge in uniform moving. Finally, the gauge symmetry and gauge transformations were discussed.

scholarly journals Lorentz transformation of a charge-current density and “relativistic polarization” of a moving current loop

2020 ◽  
Vol 35 (23) ◽  
pp. 2050135
Author(s):  
Alexander Kholmetskii ◽  
Oleg Missevitch ◽  
Tolga Yarman
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Electric Dipole ◽  
Physical Meaning ◽  
Classical Electrodynamics ◽  
Current Loop ◽  
Lorentz Transformations ◽  
Covariant Formulation ◽  
Magnetic Dipoles ◽  
A Charge

We show that the claim by Franklin (Int. J. Mod. Phys. A 35, 2050061 (2020)) with respect to the vanishing charge distribution over the perimeter of an electrically neutral moving current loop is erroneous and is based on a misinterpretation of physical meaning of Lorentz transformations. Moreover, we show that the development of nonvanishing electric dipole moment by a moving current loop (which we named as “relativistic polarization”) represents a direct implication of covariant formulation of classical electrodynamics of material media. In this respect, we analyze some subtle effects related to the motion of magnetic dipoles in an electromagnetic field and disclose their physical meaning.

scholarly journals ABOUT THE SIMULTANEOUS CO-EXISTENCE OF INSTANTANEOUS AND RETARDED INTERACTIONS IN CLASSICAL ELECTRODYNAMICS

2002 ◽  
Vol 17 (19) ◽  
pp. 2513-2518 ◽  
Author(s):  
LjUBA ŠKOVRLJ ◽  
TOMISLAV IVEZIĆ
Keyword(s):  
Magnetic Fields ◽  
Maxwell Equations ◽  
Classical Electrodynamics ◽  
Partial Derivatives ◽  
Usual Form ◽  
Electric And Magnetic Fields ◽  
Accelerated Charge

In this paper it is proved that, contrary to the results found by A.E. Chubykalo and S.J. Vlaev (Int. J. Mod. Phys.14, 3789 (1999)), the retarded electric and magnetic fields for a uniformly accelerated charge exactly satisfy Maxwell equations (ME). Furthermore, it is shown that ME are correctly written in the usual form with the partial derivatives and thus not, as proposed by Chubykalo and Vlaev, with the total derivatives.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals FORCES BETWEEN ELECTRIC CHARGES IN MOTION: RUTHERFORD SCATTERING, CIRCULAR KEPLERIAN ORBITS, ACTION-AT-A-DISTANCE AND NEWTON'S THIRD LAW IN RELATIVISTIC CLASSICAL ELECTRODYNAMICS

2008 ◽  
Vol 23 (02) ◽  
pp. 327-351 ◽  
Author(s):  
J. H. FIELD
Keyword(s):  
Special Relativity ◽  
Small Angle ◽  
Classical Electrodynamics ◽  
Classical Electromagnetism ◽  
Newtonian Gravitation ◽  
Keplerian Orbits ◽  
Rutherford Scattering ◽  
Action At A Distance ◽  
Electrodynamic Theory ◽  
Third Law

Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous intercharge force. Problems discussed include small angle Rutherford scattering, Jackson's recent "torque paradox" and circular Keplerian orbits. Results consistent with special relativity are obtained only with an instantaneous interaction. The impossibility of stable circular motion with retarded fields in either classical electromagnetism or Newtonian gravitation is demonstrated.

SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS

2002 ◽  
Vol 14 (04) ◽  
pp. 409-420 ◽  
Author(s):  
VIERI BENCI ◽  
DONATO FORTUNATO FORTUNATO
Keyword(s):  
Electromagnetic Field ◽  
Solitary Wave ◽  
Electric Field ◽  
Solitary Waves ◽  
Maxwell Equations ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper is divided in two parts. In the first part we construct a model which describes solitary waves of the nonlinear Klein-Gordon equation interacting with the electromagnetic field. In the second part we study the electrostatic case. We prove the existence of infinitely many pairs (ψ, E), where ψ is a solitary wave for the nonlinear Klein-Gordon equation and E is the electric field related to ψ.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

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