Determination of currents in flat superconductors

Explicit expressions are given for the current I(y,z) in a flat superconductor when the magnetic field Hₓ(y,z) perpendicular to its surface is measured, e.g., by the Faraday effect in a thin europium selenide layer evaporated on the specimen surface. The analytical results for a long flat strip are particularly instructive, showing what type of singularities occurs in the current and field. The general solution for the current in flat conductors of arbitrary shape is given in form of an integral over Hₓ(y,z) times an integral kernel that follows from an iteration.