On the interaction of point charges in an arbitrary domain

How will the electrostatic interaction between two point charges change if they are shielded from the other by a dielectrical slab? While the physical setting of this electromagnetic problem is relatively simple, it is easy to be wronged and the correct solution is surprisingly complicated. Here we will show a general answer using the method of images, in which the electrical field are not found by solving the Poisson's equation but by superposing an infinite number of image ...

The radiation reaction problem for an electric charge moving in flat space-time of three dimensions is discussed. The divergences stemming from the pointness of the particle are studied. A consistent regularization procedure is proposed, which exploits the Poincar\'e invariance of the theory. Effective equation of motion of radiating charge in an external electromagnetic field is obtained via the consideration of energy-momentum and angular momentum conservation. This equatio...

We show how the electrical field inside the conductor changes as a function of the number of charged-particles. We show that the non-vanishing electrical field is concentrated near the surface of the conductor, at a shallow depth on the same order of magnitude as the separation between charges. Our study has illustrated the effect of charge discretization on a fundamental emergent law of electrostatics.

Point sources in (2+1)-dimensional gravity are conical singularities that modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge in the presence of point masses in (2+1)-dimensional gravity with a cosmological constant.

This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the conventional BIM. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional BIM in such a way as to cancel out the singularities associated with the Green's ...

Theories of solvation free energies often involve electrostatic potentials at the position of a solute charge. Simulation calculations that apply cutoffs and periodic boundary conditions based on molecular centers result in center-dependent contributions to electrostatic energies due to a systematic sorting of charges in radial shells. This sorting of charges induces a surface-charge density at the cutoff sphere or simulation-box boundary that depends on the choice of molecul...

Equations describing the complete series of image charges for a system of conducting spheres are presented. The method of image charges, originally described by J. C. Maxwell in 1873, has been and continues to be a useful method for solving many three dimensional electrostatic problems. Here we demonstrate that as expected when the series is truncated to any finite order N, the electric field resulting from the truncated series becomes qualitatively more similar to the correc...

The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electr...

Can we avoid molecular dynamics simulations to estimate the electrostatic interaction between charged objects separated by a nanometric distance in water? To answer this question, we develop a continuous model for the dielectric properties of water based on a functional of the polarization. A phenomenological Landau-Ginzburg Hamiltonian for the electrostatic energy of water is parameterized to capture the dipolar correlations in the fluid at the nanometric scale. We show that...

It is shown that a well-defined expression for the total electromagnetic force $f^{em}$ on a point charge source of the classical electromagnetic field can be extracted from the postulate of total momentum conservation whenever the classical electromagnetic field theory satisfies a handful of regularity conditions. Amongst these is the generic local integrability of the field momentum density over a neighborhood of the point charge. This disqualifies the textbook Maxwell-Lore...