Here's my way of looking at the jumping ring demo:
1) Consider moving a highly-conductive ring into the field of a magnet.
For times short compared to the L/R time of the ring, the flux does not
penetrate the ring. The ring is nearly 100% diamagnetic. Flux is excluded
not just from the material that makes up the ring, but from the whole
disk-shaped area encompassed by the ring.
By the same token, moving the magnet to the ring is the same as moving the
ring to the magnet. And thirdly, putting the ring in the field of an AC
electromagnet is also the same story: for times short compared to the L/R
time of the ring, the flux does not penetrate the area encompassed by the ring.
2) I like to tell people that "voltage equals flux dot" is a Maxwell
equation. (Many people find voltage and flux easier to visualize than del
cross E. My buddy Prof. Stokes assures us the two formulations are
equivalent.)
How much voltage do you think is going to be induced around this ring which
has a 1 cm^2 cross section and maybe 15 cm of circumference? Not a whole
lot. Therefore not much flux will penetrate in the limited time available
(< 1/60th of a second). If it were a superconductor the flux would *never*
penetrate. Conversely if you cut a slot in the ring (making it C-shaped)
then a voltage develops across the slot and the flux just waltzes in.
3) We know that paramagnetic (and ferromagnetic) objects are attracted
toward regions of higher magnetic field. On the other side of the same
coin, diamagnetic objects are repelled.
We can understand this repulsion in more detail using the principle of
superposition. How does the ring achieve zero flux when it is placed in
the magnetic field? The induced current in the ring creates a locally
equal and opposite field, that's how. That is, if the field of the
electromagnet is north-on-top and south-on-bottom, then the ring
contributes a field that is just the reverse. We know from playing with
bar magnets that magnets in this configuration repel.
\ /
xxx s ooo
x x o o ring, induced current
xxx n ooo
/ \
\ /
ooo N xxx
ooo xxx electromagnet, applied current
ooo S xxx
/ \
where x means current into the page and o means current out of the page.
The current in the ring is a bit less than the winding*current (N*I) in the
electromagnet because the field of the electromagnet falls off with
distance and the ring only needs to cancel the field at the place where the
ring is.
4) What about the iron core? Remember we said that ferrormagnetic
materials have lower energy when they are in a magnetic field. If the ring
is right next to the electomagnet, it cancels the field almost everywhere,
depriving the iron of this energy. When the ring moves away, more of the
iron sees an un-cancelled field, and so the energy of the system (mainly
the energy of the iron) is lowered. Therefore by the principle of virtual
work, the ring will have a force on it, and the force will be larger if we
put more iron in the core.
Fe
Fe
Fe
Fe
xxx Fe ooo
x x Fe o o ring, induced current
xxx Fe ooo
Fe
Fe
ooo Fe xxx
ooo Fe xxx electromagnet, applied current
ooo Fe xxx
Fe
Fe
============
The foregoing offers a qualitative understanding of the situation. You
don't need to do any tricky calculations, you just need to have reasonable
estimates of certain quantities.
If you want to see if this story really hangs together, you can do the
following homework:
a) Calculate the L/R time of the ring.
Extra credit: How would L and R be changed if the one-turn ring (15 cm
circumference, (1 cm)^2 cross section) were replaced by 9 turns of aluminum
wire (135 cm length, (1/3 cm)^2 = 1/9 (cm)^2 cross section) wound into a
shape equivalent to the orignal ring and shorted end-to-end?
b) What's the magnetic energy per unit volume of iron in a strong applied
magnetic field?