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Mn-Zn ferrite cores present high permeability within the kilohertz-to-megahertz frequency range. They also present high permittivities within the same frequency range. High permeabilities lead to significant permittivity measurement errors when the conventional two-parallel-electrode method is used. In contrast, high permittivities result in the deviations of measured permeabilities from their intrinsic values. This paper presents a field-circuit coupled method to study each of these two phenomena by examining a ferrite toroid with rectangular cross section. The same toroid is used to construct an inductor and a capacitor, respectively. Analytical expressions for electric and magnetic fields in, and complex power supplied to the inductor and capacitor are formulated. Results are obtained, which show that the measured permeabilities and permittivities for Mn-Zn ferrites deviate from their intrinsic values significantly. A Newton-Raphson method is then introduced to determine the intrinsic permeabilities and permittivities based on their measured values.