[theThinker (OP)]

If I move a magnet towards a superconductor ring, would a constant current be induced in the ring.

If yes,how can we calculate the current induced?

Would the electron energy be finally radiated away? 

[chris]

This is really an @alancalverd question, but in theory I would say that, yes, if you induced a current in a superconductor using a magnet then you would get persistent current.

[alancalverd]

1.Yes.

2. The current will be sufficient to oppose the applied magnetic field

3. No (at least in a perfect supercon)

[chris]

would a constant current be induced in the ring

@alancalverd - if you could zoom in to the scale of an electron and image the superconductor, would you actually see electrons drifting along through the charged, current-bearing superconductor? If so, at what speed, and is this comparable to, say, a piece of copper wire? Or does something special happen with a superconductor?

[theThinker (OP)]

1.Yes.

2. The current will be sufficient to oppose the applied magnetic field

3. No (at least in a perfect supercon)

2) The current and the drift speed will be very high. In normal resistor, the electrons can only reach a speed in the order of mm/s because of "friction" from the lattice. This opposing force causes joule heating dissipating energy. There is no "friction" within the superconductor and the free electrons freely accelerate fully by the induced E field. The induction effect is additive and it is conceivable  that the electrons may reach near c.   
3) There should be Lamor radiation - if the high constant current does not cause high radiation dissipation, then it is an experimental repudiation of Lamor's formula.

[Colin2B]

3. No (at least in a perfect supercon)

Agreed. I recall seeing results of an experiment with a 5nH ring where flux creep meant that the half life of the current was around 1000years. That's permenant for most purposes.

[alancalverd]

You can't model superconductivity as an assembly of free classical electrons, any more than you can detect Larmor radiation from a hydrogen atom: it is a quantum phenomenon. The drift speed of electrons in a superconductor is pretty much the same as in the conducting state, but they act as a condensate rather than independent  random walkers.

[theThinker (OP)]

You can't model superconductivity as an assembly of free classical electrons, any more than you can detect Larmor radiation from a hydrogen atom: it is a quantum phenomenon. The drift speed of electrons in a superconductor is pretty much the same as in the conducting state, but they act as a condensate rather than independent  random walkers.

By just using "a quantum phenomenon", it will dismiss any attempt to try to deal with the physics from the classical viewpoint. So it is like "well, you just have to believe in me.."

In the early days, the Bohr theory was rejected as some insisted the hydrogen atom would collapse because of Lamor's formula.

1) Is there an induced current? if yes, how large is the current as compared to usual currents in conductors. How is the drift speed of the electrons?
2) Does repeated induction cause a greater current and magnetic strength.

[alancalverd]

Science is different from politics, philosophy or religion. You don't have to believe anything - indeed the opposite is true. If the hypothesis does not fit the facts, the hypothesis is wrong. As you say, the Bohr atom was almost good enough for chemistry and early nuclear physics, but was quickly abandoned on account of its inherent instability, in favor of the quantised orbital model that works for crystallography, organic stereochemistry, and infrared spectroscopy too.

Observation: currents persist for many years in superconductors. As you say, you can't explain this with any classical model, but the Bardeen-Cooper-Schreiffer quantum model does it very well, and is worth studying because it's the basis for a lot of everyday technology (at least in the medical world).

[evan_au]

1) Is there an induced current? if yes, how large is the current as compared to usual currents in conductors. How is the drift speed of the electrons?

A magnet approaching a superconductor will induce a current that cancels the external field. Even though the resistance is zero, the current is not infinite, as you only need a finite current to oppose a finite external magnetic field.

The charge carriers in a normal metal are electrons with a charge of -1, typically 1 free electron per atom.

As I understand it, the charge carriers in a conventional (BCS) superconductor are pairs of electrons with a charge of -2, on average 1 Cooper Pair per 2 atoms.

So the speed of the charge carriers will be the same in a metal when it is carrying a constant current, whether it is conducting normally or when it is cooled to act as a superconductor.

See: https://en.wikipedia.org/wiki/Superconductivity#Conventional_theories_.281950s.29

2) Does repeated induction cause a greater current and magnetic strength.

As the magnet approaches, the supercurrent grows to cancel the approaching magnetic fields (Meissner effect).
If you withdraw the magnet, ready for another "repeat", the supercurrent drops back to zero. So repeated application of the same magnet merely creates the same current.

If you instead bring in one magnet, then an extra one, and another one, the supercurrent increases each time. But the magnetic field inside the body of the superconductor remains at zero, due to the Meissner effect.

Adding extra external magnets only works up to a critical field, where the superconductivity disappears. There is a different critical field H_c for each type of superconductor.

See H_c column in: https://en.wikipedia.org/wiki/List_of_superconductors

[theThinker (OP)]

1) Is there an induced current? if yes, how large is the current as compared to usual currents in conductors. How is the drift speed of the electrons?

A magnet approaching a superconductor will induce a current that cancels the external field. Even though the resistance is zero, the current is not infinite, as you only need a finite current to oppose a finite external magnetic field.

The charge carriers in a normal metal are electrons with a charge of -1, typically 1 free electron per atom.

As I understand it, the charge carriers in a conventional (BCS) superconductor are pairs of electrons with a charge of -2, on average 1 Cooper Pair per 2 atoms.

So the speed of the charge carriers will be the same in a metal when it is carrying a constant current, whether it is conducting normally or when it is cooled to act as a superconductor.

See: https://en.wikipedia.org/wiki/Superconductivity#Conventional_theories_.281950s.29

2) Does repeated induction cause a greater current and magnetic strength.

As the magnet approaches, the supercurrent grows to cancel the approaching magnetic fields (Meissner effect).
If you withdraw the magnet, ready for another "repeat", the supercurrent drops back to zero. So repeated application of the same magnet merely creates the same current.

If you instead bring in one magnet, then an extra one, and another one, the supercurrent increases each time. But the magnetic field inside the body of the superconductor remains at zero, due to the Meissner effect.

Adding extra external magnets only works up to a critical field, where the superconductivity disappears. There is a different critical field H_c for each type of superconductor.

See H_c column in: https://en.wikipedia.org/wiki/List_of_superconductors

I have just read the wiki article on the Meissner effect. What I found is superconductivity is complicated and there is no straightforward explanation. Even too large a current may destroy superconductivity.

So I think usual Faraday induction may not apply exactly. But I still think the drift current here is much higher than usual; but they don't use drift velocity anymore but "... and ϕ is the phase of the condensate wave function. ... ":
https://physics.stackexchange.com/questions/36053/relativistic-drift-velocity-of-electrons-in-a-superconductor
So they bypass any drift velocity by using electron as waves."
   
"@HolgerFiedler 1) There is no B field inside a superconductor. In the case of vortices the B field goes through the vortex core, where the superfluid density is small. The field and current distribution in a   superconducting wire or coil are complicated, but the main observation is that the current is concentrated near the surface of the wire. 2) There is no radiation (just like in an atom), the electrons are in a quantum state with fixed L. – Thomas Dec 30 '15 at 2:40 "

I don't know why people still love the Lamor's formula so much.