Related papers: Do we need to modify Maxwell's equations?
Despite the success of Maxwell's electromagnetism in the description of the electromagnetic interactions on small scales, we know very little about the behaviour of electromagnetic fields on cosmological distances. Thus, it has been…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero…
A fixed electric charge is an electric current relative to a moving magnetic field, so that it is subjected to the force of the moving magnetic field. This means that not only time-varying magnetic field produces electric field, but moving…
In this paper we use the classical electrodynamics to show that the Lorenz gauge can be incompatible with some particular solutions of the d Alembert equations for electromagnetic potentials. In its turn, the d Alembert equations for the…
Gauge transformations are potential transformations that leave only specific Maxwell fields invariant. To reveal more, I develop Lorenz field equations with full Maxwell form for nongauge, sans gauge function, transformations yielding…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
Requiring covariance of Maxwell's equations without {\it a priori} imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules,…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
This study discusses the scale transformation of electromagnetic fields and trajectories of ions in radio-frequency linear accelerators. We will obtain a condition for mechanical similarity, where Maxwell equations with source terms and the…
We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…
The complex Lorentz force is introduced and extended to include magnetic scalar. This scalar is found to be associated with a prevailing magnetic field permeating the whole space. It also introduce an extra force in Lorentz complex force.…
We propose a modification of Maxwell's macroscopic fundamental set of equations in vacuum in order to clarify Faraday's law of induction. Using this procedure, the Lorentz force is no longer separate from Maxwell's equations. The Lorentz…