Braking of a magnetic dipole moving with an arbitrary velocity through a conducting pipe

Lectures introducing students to electromagnetic induction phenomena often feature the popular experiment in which a small magnet falling down a long conducting pipe is markedly decelerated by the retarding force due to Foucault eddy currents arising in the pipe. In this paper, a formula for the retarding force, valid both for low velocities (when the force is proportional to the velocity $v$ of magnet motion) and high velocities (when it first decreases as $v^{-1}$ and then as $v^{-1/2}$), is derived. The last two regimes are analogous to the collisionless (and hence unbounded) acceleration of plasma electrons and have not been previously described in the literature. The calculation of the retarding force in the presence of a longitudinal cut in the pipe wall is carried out, and experiments to measure this force are discussed.