Superconductors and the Meissner Effect

In summary, the Meissner Effect explains the difference between a perfect conductor and a superconductor, where the latter expels the magnetic field in its superconducting state while the former does not. This expulsion occurs due to the lower energy state of the superconducting state, allowing for the creation of induced currents and a persistent current in the absence of resistance. The Maxwell equations are not violated in this process. However, there may be confusion about the role of the external magnetic field in inducing these currents, as it does not vary with time.
  • #1
crissyb1988
42
0
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!
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
mfb said:
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.

mfb said:
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
 
  • #5
M Quack said:
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.

M Quack said:
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?
 
  • #6
crissyb1988 said:
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.
 
  • #7
DrDu said:
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?
[tex]\nabla\times E=\frac{-\partial B}{\partial t}[/tex]
DrDu said:
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
 
  • #8
DrDu said:
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.
 
  • #9
crissyb1988 said:
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?
[tex]\nabla\times E=\frac{-\partial B}{\partial t}[/tex]

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/Vibrating_sample_magnetometer
 
Last edited:

What is a superconductor?

A superconductor is a material that can conduct electricity with zero resistance when cooled below a certain temperature, known as its critical temperature. This means that electrical currents can flow through a superconductor without any energy loss or heat generation.

What is the Meissner effect?

The Meissner effect is a phenomenon that occurs when a superconductor is placed in a magnetic field. The magnetic field is completely expelled from the inside of the superconductor, causing it to float or levitate above a magnet. This effect is a result of the zero resistance and perfect diamagnetism of superconductors.

What are the applications of superconductors?

Superconductors have a wide range of applications, including in medical imaging equipment such as MRI machines, in particle accelerators, and in high-speed trains. They are also being studied for use in energy storage and transmission, as well as in quantum computing.

What is the difference between Type I and Type II superconductors?

Type I superconductors have a single critical temperature below which they exhibit zero resistance and perfect diamagnetism. They also have a sharp transition between the superconducting and normal state. Type II superconductors, on the other hand, have two critical temperatures and can exhibit both perfect diamagnetism and partial flux pinning.

Can superconductivity be achieved at room temperature?

Currently, superconductivity can only be achieved at very low temperatures, typically below -200°C. However, researchers are constantly working to discover or create materials that can exhibit superconductivity at higher temperatures, with the eventual goal of achieving room temperature superconductivity.

Similar threads

  • Atomic and Condensed Matter
Replies
3
Views
1K
  • Atomic and Condensed Matter
Replies
6
Views
1K
Replies
6
Views
1K
Replies
2
Views
1K
  • Atomic and Condensed Matter
Replies
7
Views
2K
  • Atomic and Condensed Matter
Replies
2
Views
1K
Replies
2
Views
3K
  • Atomic and Condensed Matter
Replies
3
Views
3K
Replies
1
Views
598
  • General Discussion
2
Replies
54
Views
3K
Back
Top