  Recent precision measurements of mesoscopic persistent currents in
normal-metal rings rely on the interaction between the magnetic moment
generated by the current and a large applied magnetic field. Motivated by this
technique, we extend the theory of mesoscopic persistent currents to include
the effect of the finite thickness of the ring and the resulting penetration of
the large magnetic field. We discuss both the sample-specific typical current
and the ensemble-averaged current which is dominated by the effects of
electron-electron interactions. We find that the magnetic field strongly
suppresses the interaction-induced persistent current and so provides direct
access to the independent-electron contribution. Moreover, the technique allows
for measurements of the entire distribution function of the persistent current.
We also discuss the consequences of the Zeeman splitting and spin-orbit
scattering, and include a detailed and quantitative comparison of our
theoretical results to experimental data.
