Methods for calculating the electromagnetic fields from a known source distribution: application to lightning

Two different techniques (monopole and dipole) for calculating the electric and magnetic fields from a distribution of currents and charges are discussed. Both techniques have been used for calculating the fields from lightning. A simple lightning return stroke current model, consisting of a square current pulse traveling up a vertical antenna above a ground plane, is used to compare the two techniques. Analytical expressions are obtained for the fields using each technique. These expressions are shown to be numerically equivalent, but the authors are unable to prove their equivalence analytically. It is concluded that the monopole and the dipole techniques can both be derived from Maxwell's equations and hence that both are correct. In attempting to dispel the apparent confusion that has existed regarding the validity of the monopole technique, the authors show that the monopole approach, as discussed in the literature, is applicable only to upward-traveling current waves and hence is not particularly useful in the realistic modeling of lightning return strokes