  The critical state in a superconducting thin circular disk with an arbitrary
magnetic field dependence of the critical sheet current, Jc(B), is analyzed.
With an applied field Ba perpendicular to the disk, a set of coupled integral
equations for the flux and current distributions is derived. The equations are
solved numerically, and flux and current profiles are presented graphically for
several commonly used Jc(B) dependences. It is shown that for small Ba the flux
penetration depth can be described by an effective Bean model with a
renormalized Jc entering the leading term. We argue that these results are
qualitatively correct for thin superconductors of any shape. The results
contrast the parallel geometry behavior, where at small Ba the B-dependence of
the critical current can be ignored.
