Magnetic Fields in Small Ferrite Bodies with Applications to Microwave Cavities Containing Such Bodies

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Abstract
The microwave magnetic field in a small ferrite sphere and thin circular cylinder is found in first approximation. In a circularly polarized exciting field the internal field is again circularly polarized. The ratio of the internal field to the exciting field is 3(µ±α+2)-1 for the sphere and 2(µ±α+1)-1 for the cylinder. When the exciting field is linearly polarized the internal field is elliptically polarized. The expressions derived are applied to the calculation of the detuning and change of Q of microwave resonators containing ferrite spheres, cylinders and discs. Conversely they provide a means for the calculation of the elements of the permeability tensor from the experimentally observable change in cavity characteristics. The ferromagnetic resonant frequencies calculated from the present formulas are in agreement with those obtained by Kittel by the use of demagnetizing factors.