Lagrangian and energy for nonlinear dielectrics

Abstract

Variational formulations for nonlinear dielectrics in the static approximation are elaborated. The Lagrangian is determined in connection with the general isotropic constitutive relation D = ε(E² )E and a free-charge which depends on the electric potential. This general result is then specialized to two situations where electrical interactions hold between charged conductors into a nonlinear dielectric. Moreover, it is shown that the diminishing of the energy, by the introduction of an uncharged conductor, still occurs.