  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 a
force balance equation. In the second part we present numerical results for the
Hall conductivity of the 2DEG in a periodic array of flux vortices. We find
characteristic peaks in the Hall conductance, when plotted against the filling
fraction. It is argued that the peaks can be interpreted in terms of
``topological charge'' piling up across local and global gaps in the energy
spectrum.
