Our motivation is to consider an electromagnetic Lagrangian density Lq, 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∈(6/5,2). We also study the electrostatic problem in the presence of an assigned magnetic field for q∈[1,2).
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d’Avenia et al. (2024) studied this question.
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