Interaction between two point-like charges in nonlinear electrostatics

TL;DR

This paper investigates the electrostatic interaction of two point charges within a nonlinear QED-inspired model, revealing a modified force law that weakens the Coulomb singularity at short distances.

Contribution

It derives the interaction energy and force law for two charges in a nonlinear electrostatic model, showing a weaker singularity than Coulomb's law at close proximity.

Findings

Force between charges scales as R^{-2/3} at short distances.

Interaction energy follows a + b R^{1/3} law near zero separation.

Field energy remains finite due to nonlinearity.

Abstract

We consider two point-like charges in electrostatic interaction between them within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them $R$ is much smaller than the observation distance $r:$ with the linear accuracy with respect to the ratio $R/r$, and in the opposite approximation, where $R\gg r,$ up to the the term quadratic in the ratio $r/R$. The consideration fulfilled proposes the law $a+b R^{1/3}$ for the energy, when the charges are close to one another, $R\rightarrow 0$. This leads to the singularity of the force between them to be $R^{-2/3}$, which is weaker than Coulomb law $R^{-2}$.