  The distribution of the transport current in a superconducting filament
aligned parallel to the flat surface of a semi-infinite bulk magnet is studied
theoretically. An integral equation governing the current distribution in the
Meissner state of the filament is derived and solved numerically for various
filament-magnet distances and different relative permeabilities. This reveals
that the current is depressed on the side of the filament adjacent to the
surface of the magnet and enhanced on the averted side. Substantial current
redistributions in the filament can already occur for low values of the
relative permeability of the magnet, when the distance between the filament and
the magnet is short, with evidence of saturation at moderately high values of
this quantity, similar to the findings for magnetically shielded strips.
