Meissner-London state in superconductors of rectangular cross section in aperpendicular magnetic field

The Meissner state with finite London penetration depth is analyzed for pla telet samples of rectangular cross section in a perpendicular magnetic fiel d. The exact two-dimensional numerical solution of the London equation is e xtended analytically to the realistic three dimensional case. Data obtained on Nb cylinders and foils, as well as single crystals of Y-Ba-Cu-O and Bi- Sr-Ca-Cu-O, are in a good agreement with the model. The results are particu larly relevant for magnetic susceptibility, rf, and microwave resonator mea surements of the magnetic penetration depth in high-T-c superconductors.