Born-Infeld electrostatics in the complex plane

Abstract

The complex method to obtain 2-dimensional Born-Infeld electrostatic solutions is presented in a renewed form. The solutions are generated by a holomorphic seed that makes contact with the Coulombian complex potential. The procedure is exemplified by solving the Born-Infeld multipolar configurations. Besides, it is shown that the attractive force between two equal but opposite charges is lower than its Coulombian partner; it decreases up to vanish when the charges approach each other below a distance ruled by the Born-Infeld constant.

15 pages, 4 figures

References in corpus (4)

• On non-abelian generalisation of Born-Infeld action in string theory
• Testing Born-Infeld electrodynamics in waveguides
• Anisotropic effects of background fields on Born-Infeld electromagnetic waves
• 2D Born-Infeld electrostatic fields

Cited by in corpus (7)

• On the Quasi-Linear Elliptic PDE $-\nabla \cdot (\nabla u/\sqrt{1-|\nabla u{|}^2})=4\pi {\sum }_k{a}_k{\delta }_{s_k}$ in Physics and Geometry
• Lightlike shell solitons of extremal space-time film
• Two-dimensional solutions for Born-Infeld fields
• Exact self-similar solutions in Born-Infeld theory
• Approximated solutions to Born-Infeld dynamics
• Determinantal Born-Infeld Coupling of Gravity and Electromagnetism
• Non-perturbative aspects of particle acceleration in non-linear electrodynamics