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Exact multicentered solutions to the governing equations of the Born--Infeldnonlinear theory of electrodynamics describing distributions of electric,magnetic, and dyonic point charge sources are constructed explicitly for thefirst time. The method of construction may effectively be adapted to obtainsuch solutions in generalized theories as well. As a consequence, the solutionsunveil that, in order to achieve a balance between such multicentered electricor magnetic point charge distribution in equilibrium, a static magnetic orelectric current must be present, resulting in non-conservativeness of theinduced electric or magnetic intensity field, respectively and universally.Moreover, it is also shown that the methods of construction and conclusionsdrawn in the multicentered situation may be extended to obtain exact solutionsand similar conclusions, explicitly, in the situation of continuouslydistributed charge source problems.

annals of physics

Exact Multicentered Static Point Charge Source Distributions in the  Born-Infeld Theory of Nonlinear Electromagnetism and Presence of Electric and  Magnetic Currents