This Demonstration shows a cylindrical magnet falling inside a conducting pipe. This fall is damped by the opposing force due to eddy currents generated in the conducting pipe.
Two models are used for the calculations: the pointdipole model of a magnet [1–3] (model 1) and the exact cylindrical magnet model [4, 5] (model 2). The cylindrical magnet model contains a double integral; therefore, calculation is very slow. The results of both models coincide when and both equal 1.6. = pipe length, = outer diameter of the pipe, = thickness of the pipe wall, = radius of the magnet, = height of the magnet, = volume of the magnet, = remnant field. , , , terminal velocity, , drag coefficient for infinite pipe (pointdipole models), , , inner and outer radius of pipe, volume of magnet, = conductivity of metallic pipe, , drag force. , drag force for finite pipe (pointdipole model). , drag coefficient for infinite pipe (pointdipole model). The velocity was found as the solution of the equation of motion by an iterative method: . [1] B. A. Knyazev, I. A. Kotelnikov, A. A. Tyutin and V. S. Cherkassky, "Braking of a Magnetic Dipole Moving with an Arbitrary Velocity through a Conducting Pipe," PhysicsUspekhi, 49(9), 2006 pp. 937–946. doi:10.1070/PU2006v049n09ABEH005881. [2] A. K. Thottoli, M. Fayis, T. C. Mohamed, T. Amjad, P. T. Shameem and M. Mishab, "Study of Magnet Fall through Conducting Pipes Using a Data Logger," SN Applied Sciences, 1(9), 2019 1050. doi:10.1007/s424520191086z. [3] C. S. MacLatchy, P. Backman and L. Bogan, "A Quantitative Magnetic Braking Experiment," American Journal of Physics, 61(12), 1993 pp. 1096–1101. doi:10.1119/1.17356. [4] N. Derby and S. Olbert, "Cylindrical Magnets and Ideal Solenoids," American Journal of Physics, 78(3), 2010 pp. 229–235. doi:10.1119/1.3256157. [5] Q. L. Peng, S. M. McMurry and J. M. D. Coey, "Axial Magnetic Field Produced by Axially and Radially Magnetized Permanent Rings," Journal of Magnetism and Magnetic Materials, 268(1–2), 2004 pp. 165–169. doi:10.1016/S03048853(03)004943.
