ELECTRIC-FIELD CREATED BY A CIRCUMFERENTIAL SINUSOIDAL CHARGE-DENSITY-WAVE ON THE SURFACE OF A CYLINDER

The paper is concerned with the calculation of the electric field crea ted by a distribution of charge, sinusoidal around the circumference a nd constant longitudinally, on an infinitely long cylinder. Interest i n the detailed analysis of this field was stimulated by the considerat ion of the field set up by the stator of a dielectric motor which had previously been constructed. Its stator consists of a number of conduc ting bars fixed longitudinally to a cylindrical surface, and connected in sequence to the lines of a three-phase supply. Such a stator produ ces a field essentially similar to that set up by the charged cylinder . Analysis shows that the field in space is constant at a given radius and, except in the charged surface itself, is everywhere rotating at an angular velocity determined by the speed of rotation of the cylinde r, or in the case of the stator, by the frequency of the mains supply. The field has its maximum magnitude immediately adjacent to the charg ed surface, and diminishes with distance from it, except for one speci al case. The cause of the rotating field at every point in space is th e rotation of the field patterns resulting from the charges on the cyl indrical surface. This pattern is quite complex, and the equations of its field lines are derived analytically.