Radiating Systems, Multipole Fields and Radiation — John David Jackson
Physics — E&M · spherical-cavity-resonant-modes
Problem
A spherical hole of radius a in a conducting medium can serve as an electromagnetic resonant cavity.
(a) Assuming infinite conductivity, determine the transcendental equations for the characteristic frequencies ωlm of the cavity for TE and TM modes.
(b) Calculate numerical values for the wavelength λlm in units of the radius a for the four lowest modes for TE and TM waves.
(c) Calculate explicitly the electric and magnetic fields inside the cavity for the lowest TE and lowest TM mode.