# Superconductors and the Meissner Effect

by crissyb1988
Tags: conductor, effect, meissner, meissner effect, perfect conductor, superconductor, superconductors
 P: 40 So I'm a little confused about the Meissner Effect. If we have both a perfect conductor and a superconductor (both above Tc) and place them in a magnetic field and lower their temperatures so they exhibit their respective properties, the magnetic field inside the perfect conductor persists whilst the field inside the superconductor is expelled. Now the perfect conductor is doing what we expect, there is no changing magnetic field and therefore no induced currents to counteract the field inside. Now take the case of the superconductor, it is said that current at the surface are induced and expel the field inside... but how does this happen with no changing magnetic field. Doesn't this violate conservation of energy and Maxwell's equations? Wikipedia and hyperphysics calls this the Meissner effect but there is little to no explanation of what exactly is happening. So what is happening? Is energy conserved because the original internal field is now on the outside? (I'm guessing this is what they mean by "expelled") But how does it expel this field? Thoughts, explanations, am I missing something? Thanks guys!
 Mentor P: 10,499 What is a "perfect conductor", and how does it differ from a superconductor? Anyway: Electrons (or pairs of them) are "moving" at all temperatures, in superconductors they just move in such a way that no field enters the material. I doubt that calculated the total energy of the whole system, so where do you see a problem with energy conservation? If you cool the material, the system is not closed anyway. The Maxwell equations are not violated, electric currents influence the magnetic field. Here is a sketch, and Wikipedia has an article about it.
 P: 627 OK, this is a bit hand-waving, but anyways: In a superconducting material at low temperature, the superconducting state has a lower energy than the normal-conducting state. You can interpret this as the binding energy of the cooper pairs. So upon going through the superconducting phase transition when cooling down, some small amount of energy becomes available to expel the magnetic field from the superconducting region. As far as the Maxwell equations are concerned: Within the superconducting region, at the phase transition the magnetic field is expelled, i.e. it goes from finite to zero. So it clearly varies with time, because it takes a finite time to change the temperature. Hence there will be a dB/dt and an induced emf. That emf leads to a persistent current as the superconductor has no the resistance. In a normal perfect conductor there is no energetic incentive to expel the magnetic field from the material, so nothing happens.
P: 40

## Superconductors and the Meissner Effect

 Quote by mfb What is a "perfect conductor", and how does it differ from a superconductor?
The Meissner effect is the main difference. Because according to Maxwell's equations a static field doesn't create a current and therefore no mag field is expelled from the bulk of the material.

 Quote by mfb Anyway: Electrons (or pairs of them) are "moving" at all temperatures, in superconductors they just move in such a way that no field enters the material. I doubt that calculated the total energy of the whole system, so where do you see a problem with energy conservation? If you cool the material, the system is not closed anyway. The Maxwell equations are not violated, electric currents influence the magnetic field.
I wasn't sure about apparent breaking of energy conservation laws, and of course we don;t have a closed system.

There is a different between saying "the cooper pairs are always moving" (could be vibrating etc.) and "there is always current flowing". Not sure what you are getting at. If there are always currents flowing in a superconductor then it would produce its own magnetic field in the presence of no external one. I thought the only way to induce a current is from a CHANGING external magnetic field... In my example the external field is static
P: 40
 Quote by M Quack In a superconducting material at low temperature, the superconducting state has a lower energy than the normal-conducting state. You can interpret this as the binding energy of the cooper pairs. So upon going through the superconducting phase transition when cooling down, some small amount of energy becomes available to expel the magnetic field from the superconducting region.
Yep that makes sense.

 Quote by M Quack As far as the Maxwell equations are concerned: Within the superconducting region, at the phase transition the magnetic field is expelled, i.e. it goes from finite to zero. So it clearly varies with time, because it takes a finite time to change the temperature. Hence there will be a dB/dt and an induced emf. That emf leads to a persistent current as the superconductor has no the resistance. In a normal perfect conductor there is no energetic incentive to expel the magnetic field from the material, so nothing happens.
My point is that the EXTERNAL magnetic field DOESN'T vary with time. If the external field isn't changing then how are currents being produced in the superconductor? These currents are responsible for expelling the external field, which hasn't changed.

Look at another example. An external magnetic field is applied when the superconductor is ALREADY in a superconducting state. In this example we have a changing magnetic field and hence we expect induced currents to cancel out the internal field. This goes by our normal understanding of induction. Do you see the difference in the two different examples?
P: 3,255
 Quote by crissyb1988 My point is that the EXTERNAL magnetic field DOESN'T vary with time.
Why should the external field be the relevant field?
The electrons see and react to both the external and the field created by the other electrons.
I think the situation is very similar to the Einstein de Haas effect where the magnetization of a ferromagnetic whisker is changed. This leads to a small torque on the whisker.
I suppose that a small grain of a substance becoming superconducting will also start to rotate if suspended in vacuo.
P: 40
 Quote by DrDu The electrons see and react to both the external and the field created by the other electrons.
If the external magnetic field is not changing over time then the electrons won't react to it. Am I wrong to apply it here?
$$\nabla\times E=\frac{-\partial B}{\partial t}$$

 Quote by DrDu I think the situation is very similar to the Einstein de Haas effect where the magnetization of a ferromagnetic whisker is changed.
I will look into this
P: 627
 Quote by DrDu I suppose that a small grain of a substance becoming superconducting will also start to rotate if suspended in vacuo.
Due to the "recoil" of the circulating electrons? That sounds interesting. Has this effect been measured?

I suppose one could try electrostatic levitation, and with a microscope rotation of a 10 micrometer sized grain could easily be observed. Pb is a type-I SC with Tc about 7K and Hc about 80mT....
Unfortunately, the lighter elements (Al, Ti) have much lower Tc, and a type-II SC will probably not work: Hc1 is tiny, and above that you get penetration of the magnetic field that probably kills the effect.
P: 627
 Quote by crissyb1988 If the external magnetic field is not changing over time then the electrons won't react to it. Am I wrong to apply it here? $$\nabla\times E=\frac{-\partial B}{\partial t}$$
Yes, this is correct. But note that B=mu H, and the applied "external" field is H, as seen in the 4th Maxwell equation. mu depends on the material.

You can actually measure the magnetization of an object by moving it though a pick-up coil in a constant magnetic field. This is called a vibrating sample magnetometer, and you can buy these off the shelf.

http://en.wikipedia.org/wiki/Vibrati...e_magnetometer

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