Standstill Electric Charge Generates Magnetostatic Field Under Born-Infeld Electrodynamics

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.

11 pages, 3 figures. In this version is update a permanent address of the author L.P.G. De Assis and information on submission publication. Submetted to International Journal of Theoretical Physics

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• Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge
• Born-Infeld Electrodynamics and Euler-Heisenberg-like Model: outstanding examples of the lack of commutativity among quantized truncated actions and truncated quantized actions
• Aspects of Magnetic Field Configurations in Planar Nonlinear Electrodynamics