This experiment is an application of Lenz's Law. Lenz's Law states that an induced current in a closed conducting loop will appear in such a direction that it opposes the change that produced it. The actual explanation of what happens with the ring is as follows: we see an increase in magnetic flux in the primary coil which induces a current in the ring. The induced current opposes this change, and sets up its own magnetic field. This opposition is in effect a repulsion (two like poles facing one another) and the reason that the ring jumps off. At a more fundamental level, Lenz's Law gives the direction of current flow, and the j X b force due to the radial component of the magnetic field gives the lift to the ring. From this latter statement, you can see that, with a very long magnetic core and an iron return path, there would be very little fringing field, and therefore very little force, even though large currents would flow in both the primary circuit and the secondary ring.