Related papers: The deceiving simplicity of problems with infinite…
The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
This paper presents results for the electric field due to a uniformly charged elliptical beam in the region outside the beam.
A contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is considered. By using methods of the theory of…
A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \cite{DaVl}. From their classification, it follows that there is an abundance of infinitesimally bendable…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general…
The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $\Pi$ from the point of view of continuum mechanics. Classically, $\Pi$ is the electric charge, but the theory is not limited…
We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response…
We consider an interaction of charged bodies under the following simplified conditions: the distribution of charge over each body is stable; the interaction of bodies is governed by electrical forces only. Physically, these assumptions can…
Classical thermodynamics and statistical mechanics describe systems in which nothing interacts with nothing. Even the highly refined theory of simple fluids does not deal very well with electrical interactions, boundary conditions, or…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Partial results obtained in a previous paper are completed to represent accurately…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
In nonlinear electrodynamics, QED included, we find a static solution to the field equations with an electric charge as its source, which is comprised of homogeneous parallel magnetic and electric fields, and a radial…