A Low-Frequency Approximation to the Maxwell Equations Simultaneously Considering Inductive and Capacitive Phenomena

For many technical examples, low-frequency approximations to the full set of the Maxwell equations are applicable. Commonly, either the displacement current density or the induced current density are neglected depending on a priori knowledge about the dominating effects for a specific problem setup. This leads to different subsets of the Maxwell equations describing inductive-resistive or capacitive-resistive systems, respectively. In this paper, a formulation combining both scenarios while maintaining the quasistationary assumption, i.e., without modeling wave propagation and radiation, is presented. The formulation is applied to a simple test model consisting of a bounded massive conductor embedded in a dielectric insulation.