Problem
You drop a small magnet inside a vertical copper tube (non-ferromagnetic). The magnet falls much more slowly than in free fall. Explain why in terms of Faraday’s law and Lenz’s law.
Solution
Varying flux. As the magnet falls, the magnetic flux through each annular cross-section of the tube changes with time (it increases as the magnet approaches, and decreases as it moves away).
Induced currents (Faraday). By Faraday-Neumann’s law, the changing flux induces circular currents in the copper (eddy currents):
Opposition to motion (Lenz). By Lenz’s law these currents generate a magnetic field that opposes the change that produced them: the tube behaves like a magnet that repels the approaching magnet and holds back the one moving away. The result is a braking force directed upwards.
Terminal velocity. The braking force grows with velocity; when it equals the weight, the acceleration vanishes and the magnet descends at a nearly constant terminal velocity. The kinetic energy missing compared with free fall is dissipated as Joule heating in the eddy currents in the copper.
Collegamenti
Argomenti: Electromagnetic induction Concetti: Lenz’s law · Faraday-Neumann-Lenz law · Eddy currents