TRANSIENT ELECTRIC AND MAGNETIC-FIELDS ASSOCIATED WITH ESTABLISHING A FINITE ELECTROSTATIC DIPOLE, REVISITED

We reexamine the analysis of Master and Uman [1] 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. From those calculated fields they concluded that such a square pulse of current had charge only at its front and rear. We show that errors were made in that analysis, correct these errors, and extend the overall analysis to include deriving the proper charge distribution, a uniform distribution along the current pulse, and plotting and discussing the correct field waveforms for two current propagation speeds, the speed of light and one-third the speed of light. The square wave of current can be considered to be composed of two step functions, time-delayed by the width of the square wave and of opposite polarity. For the case of a step function of current moving at the speed of light, the electric radiation, electric induction, and electrostatic fields sum to a total electric field intensity whose spatial components parallel and perpendicular to the current path are each composed of 1) a constant, independent of time, and 2) a linearly increasing term that equals the electrostatic field, appropriately time-delayed, produced by the time-varying point charge located at the starting point of the step function. The magnetic flux density for the step function appears as if it were the magnetostatic field from a semiinfinite line of current.