Is the Meissner effect responsible for a magnet floating above a superconductor?

[Relena]

Hi all ..

If a permanent magnet is placed on a superconducting material before cooling to the critical temperature, will this cause the magnet to float after cooling ?

if yes, where would the energy come from ?

thanks

 

[Dickfore]

yes. It comes from the energy of the magnetic field being expelled from the interior of the superconductor.

 

[Relena]

I don't get it

If I tried to place a magnet over a superconductor below critical temperature, it will require energy to force it nearer, so it will remain suspended, no energy is consumed in this process.

but in my case, the magnet will move up gaining kinetic energy, so, what will LOSE energy in this process ?

 

[f95toli]

You will boil off more liquid nitrogen. That is where the energy comes from.

 

[Dickfore]

You will boil off more liquid nitrogen. That is where the energy comes from.

Boiling requires energy, so no.

 

[cesiumfrog]

yes. It comes from the energy of the magnetic field being expelled from the interior of the superconductor.

Are you saying the total magnetic field will be reduced, rather than simply being displaced into a different region of space?

 

[Dickfore]

Are you saying the total magnetic field will be reduced, rather than simply being displaced into a different region of space?

Obviously the magnetic field in the volume where the superconductor is is reduced from a non-zero value to zero.

 

[cesiumfrog]

Obviously the magnetic field in the volume where the superconductor is is reduced from a non-zero value to zero.

Obviously, which is why I specifically asked about the entire field rather than only the trivial part.

For example, presuming the flux lines reroute around the superconductor rather than just terminating mid-space, the total field energy doesn't just trivially decrease by exactly the quantity of field-energy that would have been in the region inside the superconductor: in fact the field must get stronger in some regions (where the field lines have become more bunched up).

 

[Dickfore]

I am saying the total energy of the magnetic field will be reduced.

 

[marcusl]

Agreed. The electrons in the superconductor condense into pairs as the temperature drops below the critical temperature Tc, lowering their energy. That energy is available to expel the field lines and lift the magnet.

 

[cesiumfrog]

Agreed. [..] That energy is available to expel the field lines

So you're saying the field initially (when it is zeroed out from the superconducting region) gains (rather than loses) energy (this being further energy that the superconductor gives up in addition to heat)?
And that some of the field's energy is subsequently spent to elevate the magnet?
(If this is agreement, I must have misunderstood you or Dickfore.)

 

[marcusl]

Let's carefully define "the field" and its energy. There are internal and external portions of field when the material is normal, external only when it is SC. The field energy in the SC case must include the work of levitation--after all, the field is the only thing holding up the magnet. In fact, one talks of "magnetic pressure", and that must increase if, eg, one pushes down on the magnet.

Below the critical temperature, the electron system drops to a lower energy configuration, specifically, its Helmholtz free energy drops. Work is done by the SC in expelling the field and lifting the magnet. So the new external field likely stores more energy than was in the combination of internal and external fields beforehand. I guess that contradicts what I said in my last post

 

[Dickfore]

You need to consider only the situation only after the sample had become a SC. The important thing is that the external magnetic field is inhomogeneous. I do not think you will get levitation In a homogeneous magnetic field.

As you said, the field lines envelop the surface of the SC. But, the further you get from the magnet, the more divergent and separate they become. So, the field lines are denser below the SC than above it. But, field lines can be considered to have the property that they repel each other and want to straighten themselves. So, they effectively push the SC upwards towards points where the magnetic field is lower. This is a typical diamagnetic effect and a SC is an ideal diamagnet.

 

[DrDu]

Think first of the superconductor being cooled down with the magnet at a fixed distance. The magnetic field will reduce the critical temperature so we have to cool the superconductor more if the magnet is present than when it were not. That is what f95toli meant in post #4. When the magnet is released and moves up, it will cool down ( if isolated) or take up heat from the heat bath (e.g. liquid nitrogen).