  In this work we study the noncommutative nonrelativistic quantum dynamics of
a neutral particle, that possesses permanent magnetic and electric dipole
momenta, in the presence of an electric and magnetic fields. We use the
Foldy-Wouthuysen transformation of the Dirac spinor with a non-minimal coupling
to obtain the nonrelativistic limit. In this limit, we will study the
noncommutative quantum dynamics and obtain the noncommutative Anandan's
geometric phase. We analyze the situation where magnetic dipole moment of the
particle is zero and we obtain the noncommutative version of the
He-McKellar-Wilkens effect. We demonstrate that this phase in the
noncommutative case is a geometric dispersive phase. We also investigate this
geometric phase considering the noncommutativity in the phase space and the
Anandan's phase is obtained.
