  We provide a new approach to study the noncommutative effects on the neutral
Dirac particle with anomalous magnetic or electric dipole moment on the
noncommutative plane. The advantages of this approach are demonstrated by
investigating the noncommutative corrections on the Aharonov-Casher and
He-McKellar-Wilkens effects. This approach is based on the effective $U(1)$
gauge symmetry for the electrodynamics of spin on the two dimensional space.
The Seiberg-Witten map for this symmetry is then employed when we study the
noncommutative corrections. Because the Seiberg-Witten map preserves the gauge
symmetry, the noncommutative corrections can be defined consistently with the
ordinary phases. Based on this approach we find the noncommutative corrections
on the Aharonov-Casher and He-McKellar-Wilkens phases consist of two terms. The
first one depends on the beam particle velocity and consistence with the
previous results. However the second term is velocity-independent and then
completely new. Therefore our results indicate it is possible to investigate
the noncommutative space by using ultra-cold neutron interferometer in which
the velocity-dependent term is negligible. Furthermore, both these two terms
are proportional to the ratio between the noncommutative parameter $\theta$ and
the cross section $A_{e/m}$ of the electrical/magnetic charged line enclosed by
the trajectory of beam particles. Therefore the experimental sensitivity can be
significantly enhanced by reduce the cross section of the charge line
$A_{e/m}$.
