Related papers: Electric Potential Due to a System of Conducting S…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
We discuss the grounded, equipotential ellipse in two-dimensional electrostatics to illustrate different ways of extending the domain of the potential and placing image charges such that homogeneous boundary conditions are satisfied. In…
We demonstrate that the corrections to the classical Kelvin image theory due to finite electron screening length $\lambda$, recently discussed by Roulet and Saint Jean, Am. J. Phys. 68(4) 319, is amenable to an exact closed form solution in…
In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and…
The method of image charges is a powerful and elegant technique in electrostatics, commonly used to determine the electric field generated by point charges near conductors of various shapes. While standard problems focus on single charges…
For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple…
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known…
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the…
We present a topological mechanism of discretization, which gives for the fundamental electric charge a value equal to the square root of the Planck constant times the velocity of light, which is about 3.3 times the electron charge. Its…
We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
An image system for a point charge outside a dielectric sphere is presented for all complex values of relative permittivity $\epsilon=\epsilon'+i\epsilon''$. The standard image integral solution of a point charge outside a dielectric sphere…
A charge conserving approximation scheme determining the excitations of crystalline solids is proposed. Like other such approximations, it relies on "downfolding" of the original microscopic model to a simpler electronic model on the…
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…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
In the last decade, charging service providers are emerging along with the prevalence of electric vehicles. These providers need to strategically optimize their charging prices to improve the profits considering operation conditions of the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…