  We applied an effective approximation into Maxwell's equations with an axion
interaction for haloscope searches. A set of Maxwell's equations acquired from
this approximation describes just the reacted fields generated by the anomalous
interaction. Unlike other approaches, this set of Maxwell's equations
inherently satisfies the boundary conditions for haloscope searches. The
electromagnetic field solutions from the Maxwell's 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.
