# Exact Calculation of the Capacitance and the Electrostatic Potential Energy for a Nonlinear Parallel-Plate Capacitor in a Two-Parameter Modification of Born-Infeld Electrodynamics

## TL;DR

This paper provides an exact calculation of capacitance and electrostatic energy for a nonlinear parallel-plate capacitor within a two-parameter modified Born-Infeld electrodynamics framework, confirming weak field agreement with Maxwell theory.

## Contribution

It introduces an exact method to compute capacitance and energy in a nonlinear electrodynamics model, extending classical results to a modified Born-Infeld theory.

## Key findings

- Capacitance and energy have weak field expansions similar to Maxwell's theory.
- Results agree with Maxwell electrodynamics in the weak field limit.
- Nonlinear effects are negligible in weak electric fields.

## Abstract

The nonlinear capacitors are important devices in modern technologies and applied physics. The aim of this paper is to calculate exactly the capacitance and the electrostatic potential energy of a nonlinear parallel-plate capacitor by using a two-parameter modification of Born-Infeld electrodynamics. Our calculations show that the capacitance and the electrostatic potential energy of a nonlinear parallel-plate capacitor in modified Born-Infeld theory have the weak field expansions $C=\frac{\epsilon_{0} A}{d}+{\cal O}(q^{2})$ and $U=\frac{q^{2}}{2(\frac{\epsilon_{0} A}{d})}+{\cal O}(q^{4})$, where $q$ is the amount of electric charge on each plate of the capacitor. It is demonstrated that the results of this paper are in agreement with the results of Maxwell electrodynamics for weak electric fields. Numerical evaluations show that the nonlinear electrodynamical effects in modified Born-Infeld theory are negligible in the weak field regime.