2D Born-Infeld electrostatic fields

Abstract

The electrostatic configurations of the Born–Infeld field in the 2-dimensional Euclidean plane are obtained by means of a non-holomorphic complex mapping which captures the structure of equipotential and field lines. For multipole-like solutions, the electrostatic field reaches the Born–Infeld limit value when the field lines become tangent to an epicycloid around the origin.