Steady-State Solutions of Electromagnetic Field Problems. II. Forced Oscillations of a Conducting Sphere

The method discussed in Part I for the determination of steady-state solutions of electromagnetic problems is applied to a finitely conducting sphere as the simplest illustration involving a body of finite dimensions. The external e.m.f. is applied across an infinitesimal strip at the equator. The induced field appears as the sum of an infinite number of partials or modes. As the frequency is increased these modes become successively dominant. There are a series of resonance points. The real part of the driving-point admittance rises step-wise with increasing frequency and the behavior of the system is notably different from that of a normal circuit. Expressions are given for the power dissipated in heat and in radiation and it is shown that the complex power input at the driving point is equal to the integral of the complex Poynting vector over the surface of the sphere.