Abstract.
In 1934, Max Born and Leopold Infeld suggested and developed a nonlinear modification of Maxwell electrodynamics, in which the electrostatic self-energy of an electron was a finite value. In this paper, after a brief introduction to Lagrangian formulation of Born-Infeld electrodynamics with an external source, the explicit forms of Gauss’s law and the electrostatic energy density in Born-Infeld theory are obtained. The capacitance and the stored electrostatic energy for a parallel-plate and spherical capacitors are computed in the framework of Born-Infeld electrostatics. We show that the usual relations \( U=\frac{1}{2}C_{Maxwell}(\triangle \phi)^{2}\) and \( U=\frac{q^{2}}{2C_{{\rm Maxwell}}}\) are not valid for a capacitor in Born-Infeld electrostatics. Numerical estimations in this research show that the nonlinear corrections to the capacitance and the stored electrostatic energy for a capacitor in Born-Infeld electrostatics are considerable when the potential difference between the plates of a capacitor is very large.
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Moayedi, S.K., Shafabakhsh, M. Parallel-plate and spherical capacitors in Born-Infeld electrostatics: An analytical study. Eur. Phys. J. Plus 131, 55 (2016). https://doi.org/10.1140/epjp/i2016-16055-1
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DOI: https://doi.org/10.1140/epjp/i2016-16055-1