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An effect corresponding to the Faraday effect in natural dielectrics is predicted for a class of artificial dielectrics because of the existence of a Hall effect in the metallic components of the structure. A formula for Verdet's constant as a function of element polarizability and Hall coefficient is obtained. The resonance shift to be expected in a cavity resonator, filled with an artificial dielectric, and subjected to a strong magnetic field, is calculated. Prospects for the application of these effects are briefly considered.