  We have considered the conductivity properties of a two dimensional electron
gas (2DEG) in two different kinds of inhomogeneous magnetic fields, i.e.\ a
disordered distribution of magnetic flux vortices, and a periodic array of
magnetic flux vortices. The work falls in two parts. In the first part we show
how the phase shifts for an electron scattering on an isolated vortex, can be
calculated analytically, and related to the transport properties through the
differential cross section. In the second part we present numerical results for
the Hall conductivity of the 2DEG in a periodic array of flux vortices found by
exact diagonalization. We find characteristic spikes in the Hall conductance,
when it is plotted against the filling fraction. It is argued that the spikes
can be interpreted in terms of ``topological charge'' piling up across local
and global gaps in the energy spectrum.
