Eigenfrequencies of an Electromagnetic Spherical Cavity with an Eccentric Inner Small Sphere

Analytical expressions for the eigenfrequencies of an electromagnetic spherical cavity with an eccentric inner electrically small sphere are derived, for both magnetic and electric modes. The two spheres are perfectly conducting. Spherical vector wave functions and related addition theorems are used. The results are useful in problems connected with excitation or probing of resonant cavities. Some remarks are made about the practically best positioning of the probe, for more exact measurement of the eigenfrequency of any mode in the empty cavity. Graphical results for some of the lower order modes are given for various values of the parameters and for both kinds of modes.