Related papers: Counting Equilibria of the Electrostatic Potential

We consider the problem of determining the maximum number of common zeros in a projective space over a finite field for a system of linearly independent multivariate homogeneous polynomials defined over that field. There is an elaborate…

In this paper we considered divergence of electric and of magnetic fields for four cases: classical point charge, classical continuous charge, relativistic point and relativistic continuous charges. Results for classical and relativistic…

We analyze linear Einstein--Maxwell perturbations of the superextremal Reissner--Nordstr\"om geometry in its static Kerr--Schild rest frame, viewing it as the nonlinear self-field of a single static point charge. In optical radial…

The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution.…

We describe a seemingly unnoticed feature of the text-book Maxwell-Lorentz system of classical electrodynamics which challenges its formulation in terms of an initial value problem. For point-charges, even after appropriate renormalization,…

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations…

This article is concerned with the optimal boundary control of the Maxwell system. We consider a Bolza problem, where the quadratic functional to be minimized penalizes the electromagnetic field at a given final time. Since the state is…

Maxwell's verbal statement of Coulomb's experimental verification of his hypothesis, concerning force between two electrified bodies, is suggestive of a modification of the respective computable expression on logical grounds. This…

In his recently discovered handwritten notes on "An alternate way to handle electrodynamics" dated on 1963, Richard P. Feynman speculated with the idea of getting the inhomogeneous Maxwell's equations for the electric and magnetic fields…

It has been known for over 100 years that there is a discrepancy between Maxwell's electrodynamics and the idea of a classical electron as the ``atom'' of electricity. This incompatibility is known under the terms 4/3 problem of the…

We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a…

We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear…

We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as…

Starting from Jefimenko's equations, we consider the multipole expansions of electric and magnetic fields for a confined system of charges and currents. We analyze and comment on the calculus of radiated power, on the consistent use of…

After recalling the mathematical structure of Einstein's Hermitian extension of the gravitational theory of 1915, the problem, whether its field equations should admit of phenomenological sources at their right-hand sides, and how this…

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…

Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…

The possibility of the existence of magnetic charges is one of the greatest unsolved issues of the physics of this century. The concept of magnetic monopoles has at least two attractive features: (i) Electric and magnetic fields can be…

We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of…

We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…