  We study the correlator of two vector currents in quenched $SU\lr{2}$ lattice
gauge theory with a chirally invariant lattice Dirac operator with a constant
external magnetic field. It is found that in the confinement phase the
correlator of the components of the current parallel to the magnetic field
decays much slower than in the absence of a magnetic field, while for other
components the correlation length slightly decreases. We apply the maximal
entropy method to extract the corresponding spectral function. In the limit of
zero frequency this spectral function yields the electric conductivity of the
quenched theory. We find that in the confinement phase the external magnetic
field induces nonzero electric conductivity along the direction of the field,
transforming the system from an insulator into an anisotropic conductor. In the
deconfinement phase the conductivity does not exhibit any sizable dependence on
the magnetic field.
