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Oleg D. Jefimenko's electrodynamics textbook is unique in its approaches to deriving the electric and magnetic fields of arbitrary charge and current distributions and of an arbitrarily moving point charge. However, an uncommon form of the…
We study the structure of the zero set of a nontrivial finite point charge electrical field $F = (X,Y)$ in the plane $\mathbb R^2$. We establish equations satisfied by the possible directions for the zero sets \{X = 0\} and $\{Y = 0\}$…
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
Bound charge is a useful construct for calculating the electrostatic field of polarized material, and it represents a perfectly genuine accumulation of charge. But is such a material in every respect equivalent to a particular configuration…
A cosmology inspired structure for phase space is introduced, which leads to finitization and lattice-like discretization of position and momentum eigenvalues in a preferred, cosmic frame. Lorentz invariance is broken at very high energies,…
We develop an exact electrostatic formulation for a finite-length conducting cylindrical shell of finite thickness separating two dielectric media with arbitrary permittivity contrast. The boundary-value problem is reduced to a coupled…
We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as…
A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d-k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We…
The charge distribution at the interface between two electrolytes is studied for the case of non-vanishing ion fluxes. The analysis is an extension of the established Verwey-Niessen theory to non-equilibrium situations. Applying matched…
We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever.…
Two main approaches in particle-based simulations for modeling a charged surface are using explicit, discrete charges and continuum, uniform charges. It is well-known that these two approaches could lead to substantially distinct ionic…
The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a…
The concept of electromotive field appears in various applications in space and astrophysical plasmas. A review is given on the electromotive field highlighting our current understanding of the theoretical picture and the spacecraft…
The induced electric field $\vec{E}(\vec{x})$ during magnetic flux entry in superconductors with arbitrary cross section $\Omega$ and general critical current law, has been evaluated by integration along the vortex penetration paths.…
The concept of infinity took centuries to achieve recognized status in the field of mathematics, despite the fact that it was implicitly present in nearly all mathematical endeavors. Here I explore the idea that a similar development might…
Within no inertial frame can stationary charge exist. All charge, wherever it exists, experiences perpetual interaction with charge elsewhere and so can only exist as non-trivial current. It follows that the notion of the electrostatic…