Related papers: From electrostatic potentials to yet another trian…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…
The analytical expressions for the electromagnetic potential generated from a focusing charged particle beam are indispensable in various beam physics problems. In this article, we review the theory in detail and point out the necessary…
The electrostatic force on a spherical particle near a planar surface is calculated for the cases of a uniform electric field applied in either normal or tangential direction to the surface. The particle and suspending media are assumed to…
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference…
Ionic crystals play a central role in functional applications. Mesoscale descriptions of these crystals are based on the continuum polarization density field to represent the effective physics of charge distribution at the scale of the…
Using Poisson-Boltzmann equation and linear response theory, we derive an effective interaction potential due to a fixed charge distribution in a solution containing polyelectrolytes and point salt. We obtain an expression for the effective…
The starting point is the problem of finding the interaction energy of two coinciding homogeneous cubic charge distributions. The brute force method of subdividing the cube into $N^3$ sub-cubes and doing the sums results in slow convergence…
I derive formulas for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the…
We introduce and analyze $d$ dimensional Coulomb gases with random charge distribution and general external confining potential. We show that these gases satisfy a large deviations principle. The analysis of the minima of the rate function…
The symmedian point of a triangle enjoys several geometric and optimality properties, which also serve to define it. We develop a new dynamical coordinatization of the symmedian, which naturally generalizes to other ideal hyperbolic…
We consider random lozenge tilings on the triangular lattice with holes $Q_1,...,Q_n$ in some fixed position. For each unit triangle not in a hole, consider the average orientation of the lozenge covering it. We show that the scaling limit…
We evaluate the electrostatic interaction energy between two surfaces, one flat and the other slightly curved, in terms of the two-point autocorrelation functions for patch potentials on each one of them, and of a single function $\psi$…
We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
As an integrative and insightful example for undergraduates learning about electrostatics, we discuss how to use symmetry, Coulomb's Law, superposition, Gauss's law, and visualization to understand the electric field produced by a…
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…
This is a survey of the electrostatic potentials produced by charged straight-line segments, in various numbers of spatial dimensions, with comparisons between uniformly charged segments and those having non-uniform linear charge…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
From a common expression for the poloidal electrostatic field of a tokamak, in the limit of large aspect ratio and concentric circular flux surfaces, one may determine the associated potential. This potential satisfies Poisson's equation,…