Standstill Electric Charge Generates Magnetostatic Field Under Born-Infeld Electrodynamics

TL;DR

This paper explores how a stationary point charge in Born-Infeld electrodynamics generates a magnetostatic field due to non-linear effects, revealing complex internal structures and potential links to magnetic monopoles.

Contribution

It provides analytical solutions showing magnetostatic fields from static charges in Born-Infeld theory, highlighting non-linear effects and possible magnetic monopole connections.

Findings

A static charge can produce a magnetostatic field due to non-linearity.

Analytical solutions reveal internal structure of the charge.

Magnetostatic field vanishes in the Maxwell limit.

Abstract

The Abelian Born-Infeld classical non-linear electrodynamic has been used to investigate the electric and magnetostatic fields generated by a point-like electrical charge at rest in an inertial frame. The results show a rich internal structure for the charge. Analytical solutions have also been found. Such findings have been interpreted in terms of vacuum polarization and magnetic-like charges produced by the very high strengths of the electric field considered. Apparently non-linearity is to be accounted for the emergence of an anomalous magnetostatic field suggesting a possible connection to that created by a magnetic dipole composed of two mognetic charges with opposite signals. Consistently in situations where the Born-Infeld field strength parameter is free to become infinite, Maxwell`s regime takes over, the magnetic sector vanishes and the electric field assumes a Coulomb behavior with no trace of a magnetic component. The connection to other monopole solutions, like Dirac`s, t' Hooft`s or Poliakov`s types, are also discussed. Finally some speculative remarks are presented in an attempt to explain such fields.