Born-Infeld electrostatics in the complex plane

TL;DR

This paper presents a complex analysis method for 2D Born-Infeld electrostatics, revealing how nonlinear effects reduce the force between charges compared to Coulomb's law, especially at close distances.

Contribution

It introduces a renewed complex method for solving Born-Infeld electrostatic problems using holomorphic seeds linked to Coulomb potentials.

Findings

The attractive force between opposite charges is weaker than Coulomb's law.

Force decreases and vanishes as charges approach each other within a Born-Infeld-specific distance.

Solutions for multipolar configurations are explicitly constructed.

Abstract

The complex method to obtain 2-dimensional Born-Infeld electrostatic solutions is presented in a renewed form. The solutions are generated by a holomorphic seed that makes contact with the Coulombian complex potential. The procedure is exemplified by solving the Born-Infeld multipolar configurations. Besides, it is shown that the attractive force between two equal but opposite charges is lower than its Coulombian partner; it decreases up to vanish when the charges approach each other below a distance ruled by the Born-Infeld constant.