hey guys,
i'm sure you guys know that if you have a superconductor placed in a petri dish and you cool it below it's critical temperature BEFORE you place the magnet on top of it then when you actually put the magnet on it then you cannot help but generate relative motion between the magnet and the superconductor, in which case (you know this from module 2) eddy currents generated in the superconductor will be HUGE (since resistance =0) and this provides the magnetic repulsion force that keeps the magnet "afloat".
now, what textbooks say about "excluding external B fields" or "zero fields", etc, is generally that since the resistance of the superconductor is 0 then the eddycurrents generated INITIALLY inside it will be UNRESTRAINED which means a very large B field will be generated in opposition to the field of the magnet, now since the eddy currents are unrestrained then their kinetic energy will NOT be lost as HEAT in the superconductor (which is usually the case with eddy currents in normal metal) and so the generated opposing B field will be at its MAXIMUM possible - that is, it NULLIFIES the external B field of the magnet on top of it COMPLETELY! so there is absolutely no magnetic flux threading through the INSIDE of the superconductor once the magnet is put on or near it --> and this is what is meant by "excluding fields" or "zero fields". instead, the magnetic vectors of the magnetic can only bend around the superconductor.
One more thing: like i said before, it's easy to see how a superconductor can suspend a magnet in mid-air when the magnet is put onto the superconductor AFTER it is cooled below the critical temperature, this is of course as i mentioned due to induction. Now, the thing is, i think you are probably pondering on the problem that if you put a magnet onto the superconductor BEFORE you cool it, then after you cool the entire apparatus the magnet still levitates --> it's like spontaneous magic.
well there is an explanation, and the reason is this: (with the magnetic on top of the s.c. already) the magnet has a magnetic field associated with it at all times, even when it sits on top of the superconductor that is not yet cooled. now, when you proceed to cool the superconductor, then as the temperature drops below the critical temperature the resistance becomes 0; and what a resistance of 0 means is that the electrons in the superconductor are TOTALLY UNHINDERED to move through the lattice --> as a result, immediately below the critical temperature, you will have almost all liberated electrons inside the superconductor moving freely in RANDOM directions throughout the lattice. Now, this movement of electrons below the critical temp is in fact a RELATIVE motion between the electrons(which are charged) and the "stationary" magnetic field of the magnet that is present at all times as i said before. And once again, from here, it follows that these electrons' relative motion inside the superconductor to the magnet bends the paths of their random motion into swirls of eddy currents (by induction due to relative motion) and subsequently provides a B force that levitates the magnet on top.
so this is how "spontaneous" levitation occurs. just remember the moving electrons inside the conductor relative to the stationary magnet on top of it and you'll be fine.
and so you don't need to place the magnet on after the cooling to make sure it levitates (this is actually of practical importance in industry, and also of safety concerns).
hope that explains a bit for you
