Related papers: Maxwell Equations without a Polarization Field usi…
We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
Based on the microscopic Maxwell equations, we develop a method of description of the electric field in a spontaneously polarized isotropic nonpolar dielectric. We find the solution for the electric field $\textbf{E}(\textbf{r})$ for…
Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampere-Maxwell law. This has led to the suggestion that we should not teach students that electric and magnetic…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…
Classical electrodynamics can be divided into two parts. In the first one, with the use of a plenty of directed quantities, namely multivectors and differential forms, no scalar product is necessary. It is called premetric electrodynamics.…
Maxwell-Lorenz theory describes only vortex electromagnetic processes. Potential component of the magnetic field is usually excluded by the introduction of mathematical terms: Coulomb and Lorenz gauges. Proposed approach to the construction…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic…
The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
Electromagnetism is the energy originating from an electric charge. Our purpose is to enlarge Maxwell. Include the charge transfer phenomenology. A four bosons electromagnetism is derived. An EM completeness is achieved. The charge's set…
We propose a theoretical and computational approach to investigate temporal behavior of a nonlinear polarization in perturbative regime induced by an intense and ultrashort pulsed electric field. First-principles time-dependent density…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
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…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
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…
Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and…