Related papers: Can Maxwell's equations be obtained from the conti…
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom…
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even…
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…
Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the…
We considered the electromagnetic field of a charge moving with a constant acceleration along an axis. We found that this field obtained from the Li\'enard-Wiechert potentials does not satisfy Maxwell equations if one considers exclusively…
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…
The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the \emph{cognoscenti} of differential forms on manifolds; namely, that charge conservation…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
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…
An extension of the Helmholtz theorem is proved, which states that two retarded vector fields ${\bf F}_1$ and ${\bf F}_2$ satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences…
Retarded electromagnetic potentials are derived from Maxwell's equations and the Lorenz condition. The difference found between these potentials and the conventional Li\'{e}nard-Wiechert ones is explained by neglect, for the latter, of the…
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem…
Charges are everywhere because most atoms are charged. Chemical bonds are formed by electrons with their charge. Charges move and interact according to Maxwell's equations in space and in atoms where the equations of electrodynamics are…
It is now widely accepted that the Maxwell equations of Electrodynamics constitute a self-consistent set of four independent partial differential equations. According to a certain school of thought, however, half of these equations -…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
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…
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the…
A long-standing controversy concerning the causes of the magnetic field in and around a parallel-plate capacitor is examined. Three possible sources of contention are noted and detailed. The first is the ambiguous initial impression given…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…