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

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 $U=\frac{1}{2}{C}_{{}_{\text{Maxwell}}}(△\varphi {)}^2$ and $U=\frac{q^2}{2C_{{}_{\text{Maxwell}}}}$ 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.

arXiv comment12 pages, 2 figures

References in corpus (23)

• Electric-Magnetic Duality Rotations in Non-Linear Electrodynamics
• Born-Infeld particles and Dirichlet p-branes
• Regular black holes with a nonlinear electrodynamics source
• Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory
• Asymptotic Reissner-Nordstrom black holes
• Magnetic and electric properties of quantum vacuum
• Dilaton black holes coupled to nonlinear electrodynamic field
• Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space
• Nonlinear arcsin-electrodynamics
• Finite Field-Energy and Interparticle Potential in Logarithmic Electrodynamics
• On generalized Born--Infeld electrodynamics
• On Generalized Logarithmic Electrodynamics
• Photonic processes in Born-Infeld theory
• Nonlinear electrodynamics and black holes
• Point Charge in the Born-Infeld Electrodynamics
• Non-Abelian generalization of Born-Infeld theory inspired by non-commutative geometry
• Black holes and the classical model of a particle in Einstein non-linear electrodynamics theory
• Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations
• On nonlinear classical electrodynamics with an axionic term
• Stabilization of Radiation Reaction with Vacuum Polarization
• A Simple Derivation of Lorentz Self Force
• Analytical Calculation of Stored Electrostatic Energy per Unit Length for an Infinite Charged Line and an Infinitely Long Cylinder in the Framework of Born-Infeld Electrostatics
• Nonlocal Lagrangians for Accelerated Systems