  In this paper we give a covariant expression for Aharonov-Casher phase. This
expression is a combination of the canonical electric field, Aharonov-Casher
phase plus a magnetic field phase shift. We use this covariant expression for
the Aharonov-Casher phase to investigate the case of a neutral particle with a
non-zero magnetic moment moving in the {\it time dependent} electric and
magnetic fields of a plane electromagnetic wave background. We focus on the
case where the magnetic moment of the particle is oriented so that both the
electric and magnetic field lead to non-zero phases, and we look at the
interplay between these electric and magnetic phases.
