A current-carrying superconducting strip partly penetrated by magnetic flux and surrounded by a bulk magnet of high permeability is considered. Two types of samples are studied: those with critical current controlled by an edge barrier dominating over the pinning, and those with high pinning-mediated critical current masking the edge barrier.It is shown for both cases that the current distribution in a central flux-free part of the strip is strongly affected by the actual shape of the magnetic surroundings. Explicit analytical solutions for the sheet current and self-field distributions are obtained 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 its distance to the superconductor but only weakly on the magnetic permeability.
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