A method for determining the internal DC magnetic field inside a superconducting cavity is presented. The method relies on the relationship between the magnetic field and frequency of the Kittel mode of a ferrimagnetic sphere, hybridized in the dispersive regime of the superconducting cavity. Results were used to experimentally determine the level of screening that a superconducting Nb cavity provides as it changes from perfect diamagnetism to no screening. Two cavity geometries were tested, a cylinder and single post re-entrant cavity. Both demonstrated a consistent value of field that enters the cavity, expected to be the superheating critical field. Hysteresis in the screened field during ramp up and ramp down of the external magnetic field due to trapped vortices was also observed. Some abnormal behavior was observed in the cylindrical cavity in the form of plateaus in the internal field above the first critical field, and we discuss the potential origin of this behavior. The measurement approach would be a useful diagnosis for axion dark matter searches, which plans on using superconducting materials but needs to know precisely the internal magnetic field.

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