Motion of charged particles in a stepped magnetic field

Abstract We analyse the motion of a charged particle in a stepped magnetic field, in which two uniform regions are separated by a sharp interface. The trajectory consists of circular arcs of different radii joined at the boundary, and the mismatch of Larmor radii produces a drift along the interface. Four cases are distinguished: snake orbits for antiparallel fields and skipping orbits for parallel fields, each with two possible arc configurations. Using only elementary circular-motion geometry, we derive the drift velocity as a function of the crossing angle and the field ratio. For antiparallel fields, the drift velocity is independent of the field magnitudes; for parallel fields, it depends on their ratio and in one case has an intermediate maximum. The results can be written in a unified form. The model offers an intuitive introduction to gradient drift for advanced undergraduate students without requiring vector calculus.