  The planar quantum dynamics of spin-1/2 neutral particle interacting with
electrical fields is considered. A set of first order differential equations
are obtained directly from the planar Dirac equation with nonminimum coupling.
New solutions of this system, in particular, for the Aharonov-Casher effect,
are found and discussed in detail. Pauli equation is also obtained by studying
the motion of the particle when it describes a circular path of constant
radius. We also analyze the planar dynamics in the full space, including the
$r=0$ region. The self-adjoint extension method is used to obtain the energy
levels and wave functions of the particle for two particular values for the
self-adjoint extension parameter. The energy levels obtained are analogous to
the Landau levels and explicitly depend on the spin projection parameter.
