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

Sciences Faculty, Department of Physics, University of Mazandaran - P. O. Box 47415-416, Babolsar, Iran, ICRANet-Mazandaran, University of Mazandaran - P. O. Box 47415-416, Babolsar, Iran and ICRANet - Piazza della Repubblica 10, I-65122 Pescara, Italy

^(a) eslampanah@umz.ac.ir (corresponding author)

Received: 26 January 2021
Accepted: 23 February 2021

Abstract

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 the 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. The Born-Infeld (BI) NED theory is one of the most famous among 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 .