  We investigate nodal sets of magnetic Schroedinger operators with zero
magnetic field, acting on a non simply connected domain in $\r^2$. For the case
of circulation 1/2 of the magnetic vector potential around each hole in the
region, we obtain a charactisation of the nodal set, and use this to obtain
bounds on the multiplicity of the groundstate. For the case of one hole and a
fixed electric potential, we show that the first eigenvalue takes its highest
value for circulation 1/2.
