  We discuss the dynamics of a classical spinless quantum particle carrying
electric charge and constrained to move on a non singular static surface in
ordinary three dimensional space in the presence of arbitrary configurations of
time independent electric currents. Starting from the canonical action in the
embedding space we show that a charged particle with charge $q$ couples to a
term linear in $qA^3M$, where $A^3$ is the transverse component of the
electromagnetic vector potential and $M$ is the mean curvature in the surface.
This term cancels exactly a curvature contribution to the orbital magnetic
moment of the particle. It is shown that particles, independently of the value
of the charge, in addition to the known couplings to the geometry also couple
to the mean curvature in the surface when a Neumann type of constraint is
applied on the transverse fluctuations of the wave function. In contrast to a
Dirrichlet constraint on the transverse fluctuations a Neumann type of
constraint on these degrees of freedom will in general make the equations of
motion non separable. The exceptions are the equations of motion for
electrically neutral particles on surfaces with constant mean curvature. In the
presence of electric currents the equation of motion of a charged particle is
generally non separable independently of the coupling to the geometry and the
boundary constraints.
