Practical use of the new high transition temperature (Tc) superconductors demands that they be capable of carrying a large transport current. At the critical value (Ic) of current, the sample is full of flux; additional current creates additional flux and forces the flux line lattice, which was trapped in the material microstructure, to move continuously, which causes dissipation. The value of the magnetic field strength at the sample surface when full field penetration occurs is called H*. This paper describes noncontacting AC measurements of H* in ribbons of Pb-BiSrCaCuO coated with silver layers. The results can be described in terms of the single parameter H*, which is a function of both the ribbon thickness and sample temperature. The way in which these results can be used to develop a practical method of determining H* and Ic with spatial resolution is described.