Inter-charge forces in relativistic classical electrodynamics: electromagnetic induction in different reference frames

Electromagnetic fields of an accelerated charge are derived from the first principles using Coulomb's law and the relativistic transformations. The electric and magnetic fields are derived first for an instantaneous rest frame of the accelerated charge, without making explicit use of Gauss's law, an approach different from that available in the literature. Thereafter we calculate the electromagnetic fields for an accelerated charge having a non-relativistic motion. The expres...

Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather ...

The unification of electricity and magnetism achieved by special relativity has remained for decades a model of unification in theoretical physics. We discuss the relationship between electric and magnetic fields from a classical point of view, and then examine how the four main relevant authors (Lorentz, Poincar\'e, Einstein, Minkowski) dealt with the problem of establishing the transformation laws of the fields in different inertial systems. We argue that Poincar\'e's deriv...

It is generally assumed that the retarded Lienard-Wiechert electromagnetic field produced by a point particle depends on the acceleration of that source particle. This dependence is not real, it is an illusion. The true electromagnetic interaction is time symmetric (half retarded and half advanced) and depends only on the positions and velocities of the electrically charged particles. A different acceleration of the retarded source particle will result in a different position...

We demonstrate how to derive Maxwell's equations, including Faraday's law and Maxwell's correction to Amp\`ere's law, by generalizing the description of static electromagnetism to dynamical situations. Thereby, Faraday's law is introduced as a consequence of the relativity principle rather than an experimental fact, in contrast to the historical course and common textbook presentations. As a by-product, this procedure yields explicit expressions for the infinitesimal Lorentz ...

In this paper it is shown that in the approach to special relativity which exclusively deals with the four-dimensional geometric quantities (4D GQs), the invariant special relativity (ISR), there is not recently posed paradox that in a static electric field a magnetic dipole moment (MDM) is subject to a torque in some frames and not in others. In the ISR, there is no need either for the change of the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D q...

Simply by assuming the first postulate of Special Relativity and by exploring Gedankenexperiments with electromagnetic forces, we suggest that there is a speed limit in the universe, which can be determined as a relation between vacuum permeability and permittivity. We also derive space contraction and time dilatation without referring to light. Finally, we argue that, based on previous works on the derivation of Lorentz s Transformation without light and from our results, it...

The force on electric and magnetic dipoles moving in vacuo is discussed in the general case of time-variable non-uniform fields and time-variable dipole moments, to first order in v/c and neglecting radiation reaction. Emphasis is given to the symmetry between electric and magnetic dipoles, justifying in general Amp\`ere's equivalence principle, and showing that the difference between gilbertian and amperian dipoles (in vacuo) is only a question of interpretation. The express...

In a recent paper [arXiv:1205.0096], we questioned the validity of the Lorentz law of force in the presence of material media that contain electric and/or magnetic dipoles. A number of authors have criticized our methods and conclusions. This paper is an attempt at answering the critics and elaborating the relevant issues in some detail.

We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's equations. They are expressed in terms of the field strengths $(E,{\cal B})$, the excitations $({\cal D},H)$, and the sources $(\rho,j)$. This fundamental set of four microphysical equations has to be supplemented by somewhat less general ...