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