Between Maxwell and Born-Infeld: the presence of the magnetic field

Abstract

Our motivation is to consider an electromagnetic Lagrangian density ${\mathcal{L}}_q$, depending on a parameter such that, for $q=1$ it corresponds to the Born-Infeld Lagrangian density and for $q=2$ it restores the Maxwell one. The model in the presence of given charge and current densities is investigated. We solve the pure magnetostatic problem for $q\in (6/5,2)$. We also study the electrostatic problem in the presence of an assigned magnetic field for $q\in [1,2)$.

18 pages, minor corrections