Eddy currents - bouncing a magnet in mid-air

Changing a magnetic field that permeates a conductor like a metal will generate eddy currents.  This is called induction, and it was discovered by Michael Faraday nearly 200 years ago.   If you move a ferromagnet near a conductor, the changing field produces eddy currents and those eddy currents create their own magnetic fields, exerting forces back on the magnet.  Here is a rather dramatic demo of this phenomenon, shamelessly stolen by me from my thesis adviser.

In the video, you can watch in slow motion as I drop a strong NdFe₁₄B₂ magnet from about 15 cm above a 2 cm thick copper plate.  The plate is oxygen-free, high-purity copper, and it has been cooled to liquid nitrogen temperatures (77 K = -196 C).   That cooling suppresses lattice vibrations and increases the conductivity of the copper by around a factor of 20 compared with room temperature.  (If cooled to liquid helium temperatures, 4.2 K, the conductivity of this kind of copper goes up to something like 200 times its room temperature value, and is limited by residual scattering from crystalline grain boundaries and impurities.)

As the magnet falls, the magnetic flux \(\Phi\) through the copper increases, generating a circumferential electromotive force and driving eddy currents.  Those eddy currents produce a magnetic field directed to repel the falling magnet.  The currents become large enough that the resulting upward force becomes strong enough to bring the magnet to a halt about 2 cm above the copper (!).  At that instant, \(d\Phi/dt = 0\), so the inductive EMF is zero.  However, the existing currents keep going because of the inductance of the copper.  (Treating the metal like an inductor-resistor circuit, the timescale for the current to decay is \(L/R\), and \(R\) is quite small.)  Those continuing currents generate magnetic fields that keep pushing up on the magnet, making it continue to accelerate upward.  The magnet bounces "in mid air".  Of course, the copper isn't a perfect conductor, so much of the energy is "lost" to resistively heating the copper, and the magnet gradually settles onto the plate.  If you try this at room temperature, the magnet clunks into the copper, because the copper conductivity is worse and the eddy currents decay so rapidly that the repulsive force is insufficient to bounce the magnet before it hits the plate.

(Later I'll make a follow-up post about other neat physics that happens while setting up this demo.)