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 ($) over right arrow (d) = kv ($) over right arrow. We show that the coefficient k(->) of the horizontally oriented magnet is about 2/3 of the coefficient k(up arrow) for the vertically oriented magnet. If the magnetic moment makes an angle h with the vertical direction, the drag coefficient k can be expressed as k = k(up arrow) cos2 theta +k(->) sin2 theta. 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. (c) 2023 Published under an exclusive license by American Association of Physics Teachers.