The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields are computed
as solutions to the Born-Infeld equa- tions. The approach yields rich internal structures that can be described in terms of the physical fields with explicit analytic solutions. This suggests that the anomalous field probably originates from a magnetic excitation in the vacuum due to the presence of the very intense electric field. In addition, the magnetic contribution has been found to exert a negative pressure on the charge. This, in turn, balances the electric repulsion, in such a way that the self-interaction of the field appears as a simple and natural classical mechanism that is able to account for the stability of the electron charge.
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 th
e 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.
