  Axions are among the most sought-after candidates for dark matter. In the
ultralight regime, they could help alleviate puzzles in small scale cosmology.
Searches for a halo of axion dark matter rely on the electromagnetic response
to a magnetic field. In this work, we resolve a number of issues in the
determination of this response by carefully solving Maxwell's equations in the
presence of an axion background. We find that the electric field induced by a
magnetic field in an axion background is significant and unsuppressed by the
size of the experiment.
