Electromagnetic force on a magnetic dipole inside an annular pipe flow

We present an illuminating example of electromagnetic flow measurement in liquid metals that is easy to analyze yet displays a remarkably good agreement with laboratory experiments. Our system involves a small permanent magnet located inside an annular pipe carrying the flow of a liquid metal. We investigate the Lorentz force acting upon the magnet using a combination of laboratory experiments with liquid metal at room temperature and a simple analytical model. We demonstrate that the measured Lorentz forces are in very good agreement with the predictions of our model over a wide range of geometry parameters. By virtue of its simplicity and close relationship to the well known “creeping magnet” classroom experiment, our system can also serve as an educational tool for introductory courses in liquid metal magnetohydrodynamics.