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A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.
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Equations to calculate the inducing scalar and vector potentials produced by inclined return strokes are presented. Equations are also given for calculating the induced voltages of overhead lines where horizontal components of inducing vector potential exist. The adequacy of the calculation method is demonstrated by field experiments. Using these equations, induced voltages on overhead lines are calculated for a variety of directions of return stroke
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Experiments on the lightning-induced voltage waveforms on an overhead wire influenced by an inclined return-stroke channel are carried out outdoors with a reduced-scale model. The measured voltages are compared with those calculated by solving the Telegrapher's equation in combination with numerical calculation of electric fields associated with return-stroke currents, and the validity of the calculations is verified. The effect of the ground conductivity on the lightning-induced voltage waveform is studied based on numerical calculations and is found to be dependent on the position of the return-stroke channel relative to the overhead wire. When a return stroke hits the ground close to the end of the overhead wire, the influence of the ground conductivity on the induced voltage waveform is significant irrespective of the inclination or the direction of the lightning channel. The degree of the influence is dependent on the inclination and the direction of the channel when a return stroke hits the ground on the side of the overhead wire
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