Eur. Phys. J. Plus (2016) 131: 55
https://doi.org/10.1140/epjp/i2016-16055-1

Regular Article

Parallel-plate and spherical capacitors in Born-Infeld electrostatics: An analytical study

Department of Physics, Faculty of Sciences, Arak University, 38156-8-8349, Arak, Iran

^* e-mail: s-moayedi@araku.ac.ir

Received: 7 December 2015
Accepted: 24 January 2016
Published online: 11 March 2016

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 and 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.