Generalized Hertz Vector in the Dissipative Electrodynamics

Abstract

In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve particular radiation processes. It indicates that the related method is sometimes more effective than the scalar and vector potential-based relations. Finally, the measurable field variables, the electric and magnetic fields, can be deduced by direct calculation from the Hertz vector. However, right now, the introduction of the Hertz vector operates if the conductive current density j = 𝜎E is neglected. We suggest a generalization by the conductive currents, i.e., when the electromagnetic field dissipates irreversibly to Joule heat. The presented procedure enables us to introduce also the Lagrangian formulation of the discussed dissipated electromagnetic waves. It paves a new way involving damping physical fields in a thermodynamic frame.