Steady-State Solutions of Electromagnetic Field Problems. I. Forced Oscillations of a Cylindrical Conductor

Abstract

The object of this investigation is a study of the current distribution in or on the surface of a conductor and its associated field under the influence of a localized e.m.f. Steady-state solutions of the field equations are found for conductors of simple geometric form. The results clarify many electromagnetic problems involving localized sources, especially in the u-h-f region, for which ordinary circuit theory fails to give a satisfactory quantitative explanation. Part I treats the problem of a straight cylindrical conductor and shows the relation of the principal and complementary waves to the nature of the exciting field. A driving point impedance is calculated for the case of an external field applied over a vanishingly short section of conductor. The driving point impedance is infinite for a conductor of infinite length and perfect conductivity. Likewise the case of a conductor of finite length bounded at either end by an infinite, perfectly conducting plane is discussed. This problem bears a direct relation to that of a hollow pipe excited by a linear antenna.