Related papers: Counting Equilibria of the Electrostatic Potential
The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
We use the isotropy of the Cosmic Microwave Background to place stringent constraints on a possible electrical charge asymmetry of the universe. We find the excess charge per baryon to be $q_{e-p}<10^{-26}e$ in the case of a uniform…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
Electrical charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of non-equilibrium thermodynamics, combined with Maxwell's…
The physical consequences of the relativistic and nonrelativistic approaches to describe the energy levels of electrons which propagate in a static homogeneous magnetic field are considered. It is shown that for a given strength of the…
In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical…
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…
Stable matching is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley. In this paper, we provide a new upper bound on…
A cornerstone of physics, Maxwell's theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and self-mass of an electron of finite extension do not obey Einstein's famous…
Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice…
Charge conservation in the theory of elementary particle physics is one of the best-established principles in physics. As such, if there are magnetic monopoles in the universe, magnetic charge will most likely be a conserved quantity like…
The Einstein-Maxwell fields of rotating stationary sources are represented by the SU(2,1) spinor potential $\Psi_A$ satisfying \[ \nabla \cdot [\Theta ^{-1}(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A)]=-2\Theta ^{-2}\vec{C}\cdot (\Psi_A\nabla…
The exact Li$\acute{e}$nard-Wiechert solutions for the point charge in arbitrary motion are shown to be null fields everywhere. These are used as a basis to introduce extended electromagnetic field equations that have null field solutions…
We consider two point charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We argue that if the two charges are equal to each other…
A new optimization framework to design steady equilibrium solutions of the Vlasov-Poisson system by means of external electric fields is presented. This optimization framework requires the minimization of an ensemble functional with…
We obtain some new upper bounds on the maximum number $f(n)$ of edges in $n$-vertex graphs without containing cycles of length four. This leads to an asymptotically optimal bound on $f(n)$ for a broad range of integers $n$ as well as a…
The remarkable geometries of ellipsoidal equipotentials and their associated gradient fields, as produced by uniformly charged straight-line segments, are discussed at an elementary level, motivated by recent treatments intended for…
The Schr\"odinger equation for a charged particle in the field of a nonrelativistic electric quadrupole in two dimensions is known to be separable in spherical coordinates. We investigate the occurrence of bound states of negative energy…
The first regular exact black hole solution in General Relativity is presented. The source is a nonlinear electrodynamic field satisfying the weak energy condition, which in the limit of weak field becomes the Maxwell field. The solution…