A current-carrying superconducting strip partly penetrated by magnetic flux
and surrounded by a bulk magnet of high permeability is considered. Two ty
pes of samples are studied: those with critical current controlled by an ed
ge barrier dominating over the pinning, and those with high pinning-mediate
d critical current masking the edge barrier. It is shown for both cases tha
t the current distribution in a central flux-free part of the strip is stro
ngly affected by the actual shape of the magnetic surroundings. Explicit an
alytical solutions for the sheet current and self-field distributions are o
btained which show that, depending on the geometry, the effect may suppress
the total loss-free transport current of the strip or enhance it by orders
of magnitude. The effect depends strongly on the shape of the magnet and i
ts distance to the superconductor but only weakly on the magnetic permeabil
ity.