On the theory of electrostatic alternators

Abstract

A more elegant method than that previously given for the solution of the equations involved in the theory of electrostatic alternators is given, and illustrated by application to an electrostatic alternator of eight inductors and eight carriers, in which each carrier as it comes in front of an inductor is connected to the next following inductor by means of a brush and insulated arm. The method can be extended to the solution of electrostatic alternators of m carriers and m inductors, where each carrier is connected to the inductor next following, also where each carrier is connected by means of brushes properly placed to the pth inductor following. It may also be applied to electrostatic alternators with m inductors and 2m, 3m, or 4m carriers, and to electrostatic alternators of the Wimshurst type. With regard to the eight inductor alternator it is shown that three waves travel around the machine with periods corresponding to the time of 2 revolutions, 1 revolution, and 2/3 revolutions. The amplitude factor for each wave per eighth revolution is calculated approximately. Finally the effect of the initial conditions (potentials) on the action of the machine is discussed. It is shown that the potentials of the inductors of the machine eventually lag π/4 behind each other.