TL;DR
This paper explores 2D Born-Infeld electrostatic fields using complex mapping, revealing how the field approaches the Born-Infeld limit and maintains finite energy, with implications for understanding nonlinear electrostatics.
Contribution
It introduces a non-analytical complex mapping method to analyze 2D Born-Infeld electrostatic configurations and describes their geometric and energetic properties.
Findings
Electrostatic fields approach the Born-Infeld limit when tangent to an epicycloid.
Total energy per unit length remains finite.
Field and equipotential lines are characterized by complex mappings.
Abstract
The electrostatic configurations of the Born-Infeld field in the 2-dimensional Euclidean plane are obtained by means of a non-analytical complex mapping which captures the structure of equipotential and field lines. The electrostatic field reaches the Born-Infeld limit value when the field lines become tangent to an epicycloid around the origin. The total energy by unit of length remains finite.
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