Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

TL;DR

This paper introduces a variable power Maxwell nonlinear electrodynamics theory that successfully removes the electric field singularity at point charges, a problem unresolved by traditional power Maxwell models, when the power is less than 1/2.

Contribution

The study demonstrates that a modified power Maxwell nonlinear electrodynamics theory can eliminate electric field singularities at point charges, extending previous models.

Findings

Electric field singularity is removed for powers less than 1/2.

The proposed theory generalizes existing nonlinear electrodynamics models.

Potential implications for finite self-energy of point charges.

Abstract

YES! We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. Born-Infeld (BI) NED theory is one of the most famous of them. However the power Maxwell (PM) NED cannot remove this singularity. In this paper, we show that the PM NED theory can remove this singularity, when the power of PM NED is less than $s<\frac{1}{2}$.