Searching for solutions to Born-Infeld equations

RAFAEL FERRARO

Bad Honnef

Congreso; 475th Wilhelm & Else Heraeus Seminar: Problems and Developments in Classical Electrodynamics; 2011

The building of Born-Infeld electrostatic configurations in the plane implies the integration of a non-holomorphic complex potential. This potential is entirely determined by the choice of a holomorphic function linking the potential to an auxiliary complex field closely related to the electrostatic field. This procedure to obtain Born-Infeld electrostatic configurations is exemplified by solving the multipoles. 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.