Transient electric and magnetic fields associated with establishing a finite electrostatic dipole, revisited

The authors reexamine the analysis of M.J. Master and M.A. Uman (1983), who derived and plotted the electromagnetic field waveforms generated by a square wave of current propagating with constant speed along a finite linear path, resulting in the formation of a finite electrostatic dipole. It was concluded that such a square pulse of current had charge only at its front and rear. The authors argue that errors were made in that analysis, correct these errors, and extend the overall analysis: (1) to show that the decomposition of the electromagnetic fields into electrostatic, induction, and radiation components on the basis of distance dependence is not general; (2) to demonstrate the use of the continuity equation in finding the charge distribution along a current path when the current distribution is known; and (3) to show how a seemingly simple analytical technique, the treatment of an abrupt step of current as a linearly rising current in the limit that the risetime goes to zero, can lead to erroneous results if there is not a good physical and mathematical understanding of all the variables involved