On the time domain solution methods in classical electromagnetics

Dragan Poljak and Mirko Jakić
Faculty of Electric Engineering, Mechanical Engineering and Naval Architecture, University of Split; Faculty of Humanities and Social Sciences, University of Split

The paper deals with the time domain techniques used within the framework of the classical field theory for the solution of electromagnetic phenomena. Direct time domain solution methods based on differential and integral equation formulations are considered. Illustrative computational examples are related to transient analysis of grounding systems and penetration of the transient electric field from dipole antennas used in ground penetrating radar (GPR) applications.

A particular emphasis is given to the solutions of the wave equations (derived from Maxwell’s equations) represented by particular integrals often referred to as the retarded potentials and the advanced potentials. The retarded potentials are related to the electromagnetic waves detected at an observation point once they are emitted from a source. The advanced solutions, on the other hand represent the waves reaching the detector before they leave the source.

Note that in applied electromagnetics the advanced potentials are always dropped out and regarded as non-physical. Nevertheless, the linear nature of the wave equation in principle allows the advanced solutions to represent radiation phenomena accurately.

On the basis of the fact that convergent waves represented by the advanced potentials, though mathematically possible, are never observed in nature (Water waves in a pond do not converge ejecting a stone…) they are eliminated by prescribing certain set of boundary and initial conditions, or even invoking the principle of causality of natural phenomena. Finally, the problem of a back-reaction force (radiation reaction force, radiation resistance) experienced by an accelerated charge (in the process of losing energy by radiation) is discussed in the paper, as well.