A magnet falling inside a conducting pipe: Dependence of the drag force on the magnet orientation

We develop a simple model to investigate the orientation-dependence of the drag force acting on a magnet falling inside a vertical conducting pipe. We approximate the magnet by a point magnet and the pipe by a two-dimensional cylindrical surface. Independent of the magnet's orientation, the drag force is proportional to its velocity: F→d=−kv→. We show that the coefficient k→ of the horizontally oriented magnet is about 2/3 of the coefficient k↑ for the vertically oriented magnet. If the magnetic moment makes an angle θ with the vertical direction, the drag coefficient k can be expressed as k=k↑ cos2θ+k→ sin2θ. When the magnet falls with a non-vertical orientation, a local charge distribution is induced in the pipe, which plays a role as important as that of the time-varying magnetic field due to the falling magnet in generating the eddy currents. The model's predictions are compared with experimental results.