Effect of magnetic field on over-doped HTc superconductors: Conflicting predictions of various HTc theories

Following the recent NMR experiments by Gorny et al., we discuss the effect of a magnetic field on the superconducting T_c and the spin pseudo-gap T^*. As a testable prediction, we argue that a spin pseudo-gap should also be observed in over-doped samples in a magnetic fied (while normally there is no pseudo-gap above T_c). We find that different theoretical approaches have marked differences in their predictions for over-doped HTc cuprates.