We applied an effective approximation into Maxwells equations with an axion interaction for haloscope searches. A set of Maxwells equations acquired from this approximation describes just the reacted fields generated by the anomalous interaction. Unlike other approaches, this set of Maxwells equations inherently satisfies the boundary conditions for haloscope searches. The electromagnetic field solutions from the Maxwells equations were evaluated for both cylindrical and toroidal cavity geometries including when the axion mass becomes ultra-light (sub-meV). A small but non-zero difference between the electric and magnetic stored energies appeared in both cases. The difference may come from an anomalous non-dissipating current induced by oscillating axions.
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