  As an example for a seemingly simple but actually intricate problem, the Bean
critical state is studied in a superconducting strip of finite thickness d and
width 2w >> d placed in an oblique magnetic field. The analytical solution is
obtained to leading order in the small parameter d/w. The critical state
depends on how the applied magnetic field is switched on, e.g., at constant
tilt angle, or first the perpendicular and then the parallel field component.
For these two basic scenarios the distributions of current density and magnetic
field are obtained in the critical states. In particular, we find the shapes of
the flux-free core and of the lines separating regions with opposite direction
of the critical currents, the detailed magnetic field lines (along the vortex
lines), and both components of the magnetic moment. The component of the
magnetic moment parallel to the strip plane is a nonmonotonic function of the
applied magnetic field.

Superconductivity