Steady-State Solutions of Electromagnetic Field Problems. III. Forced Oscillations of a Prolate Spheroid

Abstract

The method discussed in Parts I and II for the determination of steady-state solutions of electromagnetic problems is applied to a prolate conducting spheroid. An external e.m.f. is applied across the central section of the spheroid and the resultant field is represented as an infinite sum of wave modes expressed in terms of spheroidal functions. To each mode there corresponds a definite resonant frequency. As the applied frequency passes through the resonance point of a given mode, the corresponding term in the driving-point admittance changes from capacitive through a pure conductance to inductive. The sharpness of resonance increases with the eccentricity. Curves are drawn showing the behavior of the real and imaginary parts of the admittance for several values of eccentricity. The solution goes over, in the limit of zero eccentricity, to that discussed in II. When the eccentricity approaches unity one obtains a linear antenna of finite length and the driving-point impedance at the resonance frequency of the first mode is shown to be about 72 ohms.