To understand the force on the jumping ring one must account for its self-inductance, which causes an extra phase lag of the induced current. The AC current in the coil produces an alternating magnetic field, which induces an alternating current in the ring. The ring thus experiences an alternating vertical magnetic force, due to the radial component of the magnetic field. (One can also think of this as a force between the two currents, repulsive when they are parallel and attractive when they are opposite.) Without self-inductance of the ring, the induced current would lag the magnetic field by a quarter cycle, and the time averaged vertical force would vanish. The self-inductance causes an additional phase lag, hence a repulsive average force. See Jeffery & Amiri, "The Phase Shift in the Jumping Ring," TPT 46, 250(2008), for a detailed explanation.
Some demonstrations that can be performed with this apparatus: (1) JUMPING RINGS: Placing a ring over the extended primary coil core and switching it on causes the ring to jump. A smaller ring will jump higher. Cool the ring in liquid nitrogen to get a really great jump, but be careful about hitting the rear projection screen. Broken metal rings and wooden rings are unaffected. (2) RESISTIVE HEATING: Verify that there is resistive heating in the secondary ring by having a student hold it down until it gets too hot to touch! (3) A light bulb on a small coil lights up when the coil is moved over the extended core. (4) A secondary coil with small light bulb placed in a beaker on top of the secondary coil will remain lit when it is covered by water in the beaker.
An interesting historical note: This device is named for its inventor, electrical engineer Elihu Thomson, not for his better known contemporary J. J. Thomson, whose work with CRTs led to the discovery of the electron.
Water, liquid nitrogen for cooling rings, and related accessories can be available upon request.
Thanks to Prof. Ted Jacobson for assistance with this explanation.