A transport current distribution over a wide superconducting sheet is shown to strongly change in a presence of bulk magnetic screens of a soft magnet with a high permeability. Depending on the geometry, the effect may drastically suppress or protect the Meissner state of the sheet through the enhancement or suppression of the edge barrier critical current. The total transport current in the magnetically screened Meissner state is expected to compete with the critical current of the flux-filled sheet only for samples whose critical current is initially essentially controlled by the edge barrier effect.
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