Problem
A cylindrical magnet is dropped inside a vertical copper tube. An observer notes that it falls very slowly, much more slowly than it would in an identical plastic tube. (a) Why does the magnet fall so slowly in the copper tube? (b) Where does the “missing” kinetic energy go? (c) What would change if the tube were made of a superconducting material?
Solution
(a) Why it slows down. As the magnet descends, the magnetic flux through every cross-section (ideal ring) of the copper tube changes continuously. By the Faraday-Neumann law this induces swirling eddy currents in the copper, called Foucault currents. By Lenz’s law these currents circulate in the direction that opposes the change in flux: they create a magnetic field that repels the approaching magnet and attracts it as it recedes. The result is a magnetic force always directed upwards, opposing the motion, which brakes the fall (a sort of “magnetic friction”). The magnet soon reaches a terminal velocity at which the magnetic brake balances gravity. In the plastic tube, an insulator, no induced currents can flow and the magnet falls freely.
(b) Where the energy goes. The kinetic energy the magnet fails to gain is spent driving the Foucault currents in the copper, which has non-zero resistance. These currents dissipate energy by the Joule effect (): the copper heats up slightly. In practice the gravitational potential energy is converted into heat instead of kinetic energy.
(c) Superconducting tube. In a superconductor the resistance is zero: the induced currents are not dissipated by the Joule effect but persist. They completely expel the magnet’s field (Meissner effect) and generate a permanent repulsion: the magnet does not “fall braked”, but remains suspended in stable magnetic levitation above the tube, without dissipation.
Links
Topics: Electromagnetic induction Concepts: Lenz’s law · Foucault currents · Joule effect