"The problem of a steady boundary layer or sheath between a plasma and a magnetic field is considered. A self-consistent transition layer is found which joins a uniform magnetic field at plus infinity with a collisionless field-free plasma region with arbitrary velocity distribution at minus infinity, i.e., a magnetic field profile is found such that the exact particle orbits in this field produce a current which gives rise to this field. An interesting feature of the solution is that, with any nonsingular velocity distribution at minus infinity, the magnetic field the plasma extends to infinity, exponentially attenuated, into the magnetic field region. The scale of length is the Larmor radius. Electric fields arising from charge separation in the case of particles of different mass are ignored."