Exact analytical results are obtained for the magnetization of a superconducting thin strip with a general behavior Jc(B) of the critical current density. We show that within the critical-state model the magnetization as a function of applied field, Ba has an extremum located exactly at Ba= 0. This result is in excellent agreement with presented experimental data for a YBa2Cu3O7-δthin film. After introducing granularity by patterning the film, the central peak becomes shifted to positive fields, Bcp< 0, on the descending field branch of the loop. Our results show that a positive Bcpis a definite signature of granularity in superconductors.
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