On the interaction of point charges in an arbitrary domain

We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is then only due to charges within that cavity itself and to the surface charge induced on the surface of the same cavity. A similar statement holds for the exterior of the conductor. Although this is an elementary property of conductors, it is n...

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (i) We show that the electrostatic potential of a charge at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine parameter distance al...

This paper presents a simple and effective new numerical scheme for the computation of electrostatic fields exterior to a collection of close-to-touching discs. The method is presented in detail for the two-cylinder case. The key idea is to represent the required complex potential using a hybrid set of basis functions comprising the usual Fourier-Laurent expansion about each circle centre comple- mented by a subsidiary expansion in a variable associated with conformal mapping...

Two main approaches in particle-based simulations for modeling a charged surface are using explicit, discrete charges and continuum, uniform charges. It is well-known that these two approaches could lead to substantially distinct ionic distributions, whereas a systematic exploration of the origin is still absent. In this short communication, we calculate the electrostatic force of a single point charge above a planar substrate characterized by a surface charge density and die...

The Dirichlet Principle is an approach to solving the Dirichlet problem by means of a Dirichlet energy integral. It is part of the folklore of mathematics that the genesis of this argument was motivated by physical analogy involving electrostatic fields. The story goes something like this: If an electrostatic potential is prescribed on the boundary of a region, it will extend to a potential in the interior of the region which is harmonic when the electric field is in stable e...

We look at an electric charge in hyperbolic motion, and we describe some arcane geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material point particles are replaced by infinitesimal length elements along their worldlines. We show that the four-force obtained from our geometrical model is very closely related to the "electrostatic" four-force obtained from Fokker's time symmetric action.

We provide a unified geometrical origin for both boundary charges and particle dressings, with a focus on electrodynamics. The method is furthermore generalizable to QCD and gravity, and can be extended to the non-perturbative domain.

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 all the terms included in these singularities.

Exact expressions for three-dimensional potential and force yield due to uniform singularity distributed on a finite at rectangular surface have been presented. The expressions, valid throughout the physical domain, have been found to be consistent with other expressions available as special cases of the same problem. Very accurate estimates of the capacitance of a unit square plate and a unit cube have been made using them.

The electrostatic field magnitude can play a role in a variational principle similar to the role of the index of refraction in geometrical optics, allowing the determination of the electric field lines. This was identified in the context of the grounded conducting sphere image problem. Assuming the knowledge of the magnitude of the electric field, in this paper we validate this principle for the general case and explore some of its consequences.