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In the literature, three procedures have been used to calculate the electromagnetic fields from return strokes. In the first technique, the source is described only in terms of current density and the fields are expressed entirely in terms of the return-stroke current. In the second technique, the source is expressed in terms of the current and the charge densities and the fields are given in terms of both the current and the charge density. In the third technique, the fields are expressed in terms of the apparent charge density. The fields are connected to the source terms through the vector and scalar potentials. In this paper, the standard equations for the electromagnetic fields generated by an accelerating charge are utilized to evaluate the electromagnetic fields from lightning return strokes. It is shown that the total fields evaluated at any distance using these expressions are identical to those obtained using other techniques. However, the composition of the terms that vary as 1/R, 1/R2, and 1/R3 of the total electric field is different from those of other formulations. In the case of the transmission-line model, where the return stroke is described as a current pulse propagating with uniform velocity, radiation emanates only from the bottom of the channel where current is generated. When the speed of propagation is equal to the speed of light, the total field throughout the entire space becomes radiation. The procedure is also applied here to obtain the electric fields of the traveling-current-source model. The electric fields obtained for this case, too, agree with the previous study. It is also shown how the equations can be applied rather conveniently to evaluate: 1) the electromagnetic fields generated by current pulses propagating along overhead power lines; and 2) the electromagnetic fields generated by vertical conductors and towers during lightning strikes.