Meissner effect and levitation

[kelvin490]

In a field less than critical field, decreasing the temperature below the critical temperature will eliminate the magnetic field inside a superconductor and increase the magnetic field around it. (Meissner effect). But does it related to levitation effect of magnet on a superconductor? What makes it float in air?

 

[rumborak]

Lowering a superconductor into a magnet's field causes a current to be induced into the superconductor (through induction). That current creates its own magnetic field opposite to the other field, which then repel each other. That's why it floats.
If you go above critical temp, the resistance quickly shuts down the current and the magnetic field along with it. So, no more floating.

 

[kelvin490]

Lowering a superconductor into a magnet's field causes a current to be induced into the superconductor (through induction). That current creates its own magnetic field opposite to the other field, which then repel each other. That's why it floats.
If you go above critical temp, the resistance quickly shuts down the current and the magnetic field along with it. So, no more floating.

Does it related to the cancellation of magnetic field inside the superconductor? Is that the induced magnetic field cancels the the magnetic field inside superconductor so that there is no magnetic field inside (Meissner effect)?

 

[rumborak]

No. It simply has to do with the fact that the superconductor is no longer a superconductor when it's above critical temperature. It thus has normal resistance, which turns the current into plain heat in a blink of an eye.

 

[kelvin490]

In a textbook the effect is explained this way: "The diamagnetic nature of a superconductor has some interesting mechanical consequences. A paramagnetic or ferromagnetic material is attracted by a permanent magnet because the magnetic dipoles in the material align with the nonuniform magnetic field of the permanent magnet. For a diamagnetic material the magnetization is in the opposite sense, and a diamagnetic material is repelled by a permanent magnet." (University physics).

I wonder why it mentions diamagnetism? A diamagnetic material is slightly repelled by magnet but the mechanism is different from the effect of the Faraday's law of induction. Is the levitation due to diamagnetism?

 

[rumborak]

Diamagnetism is not a description of a cause, but of an effect (which can have several causes). A superconductor in the presence of a magnetic field builds up a field that is opposite to the original field. Thus, it is diamagnetic. Other materials are diamagnetic through totally different mechanisms.
No offense, but I find it kinda weird how your questions continuously search for "some other reason".

 

[kelvin490]

Diamagnetism is not a description of a cause, but of an effect (which can have several causes). A superconductor in the presence of a magnetic field builds up a field that is opposite to the original field. Thus, it is diamagnetic. Other materials are diamagnetic through totally different mechanisms.
No offense, but I find it kinda weird how your questions continuously search for "some other reason".

Actually the way you explained it is just what I thought about the superconductivity but I get confused when I read more. Since for type 1 superconductor the magnetic field becomes zero inside the superconductor when it cools below critical temperature, I wonder whether we can understand it as a cancel out effect of magnetic field.

 

[f95toli]

A superconductor is effectively diamagnetic. The reason why this is important is that it allows for the magnet to "float" on its own field in a stable configuration. If you try levitate one magnet by placing it on top of another magnet with same polarity you will (obviously) find that they repel each other, but you will also find that it is impossible to find a position where this configuration is stable, the magnet will never float but will want to move to one side etc. In can in fact be shown that it impossible to find a stable configuration (Earnshaw's theorem) unless you have a diamagnet (as opposed to ferro- or paramagnetism). This is why the diamagnetism is important.

 

[rumborak]

A superconductor is effectively diamagnetic.

That makes it sound as if it isn't really diamagnetic. Superconductors are diamagnets, by the very definition of the term diamagnetic.

 

[rumborak]

Actually the way you explained it is just what I thought about the superconductivity but I get confused when I read more. Since for type 1 superconductor the magnetic field becomes zero inside the superconductor when it cools below critical temperature, I wonder whether we can understand it as a cancel out effect of magnetic field.

I mean, yes, the internal magnetic field is zero because the induced current, which runs mostly on the surface of the superconductor, creates an internal magnetic field that exactly cancels the external field.
But, that is unrelated to the levitation effect. If a superconductor could be superconducting while having its current go through the whole thing (and thus have an internal magnetic field), it would still levitate/be diamagnetic.

 

[f95toli]

That makes it sound as if it isn't really diamagnetic. Superconductors are diamagnets, by the very definition of the term diamagnetic.

I guess that depends on how you see it. I just meant that superconducting materials are not intrinsically diamagnetic in the same way as some elements (say oxygen) and compounds are diamagnetic; the underlying mechanism is quite different. .

 

[rumborak]

Of course the underlying mechanisms are different, but "diamagnetic" refers to the effect ("dia" = opposite) not the cause.

 

[kelvin490]

I mean, yes, the internal magnetic field is zero because the induced current, which runs mostly on the surface of the superconductor, creates an internal magnetic field that exactly cancels the external field.
But, that is unrelated to the levitation effect. If a superconductor could be superconducting while having its current go through the whole thing (and thus have an internal magnetic field), it would still levitate/be diamagnetic.

Of course the underlying mechanisms are different, but "diamagnetic" refers to the effect ("dia" = opposite) not the cause.

I think I am clear about what leads to the repulsion and the word "diamagnetic" in that textbook just means the effects and says nothing about the intrinsic mechanism.

I have another question as rumborak mention the induced current creates an internal magnetic field that exactly cancels the external field. If the superconductor behave like this it is actually a very strong electromagnet and it also has its north and south pole. Why it can be levitated so stably while a permanent magnet cannot?

 

[rumborak]

The simple answer is, the superconductor's magnetic field is dynamic, and thus counteracts fluctuations. A regular magnet has a static field.

 

[f95toli]

I have another question as rumborak mention the induced current creates an internal magnetic field that exactly cancels the external field. If the superconductor behave like this it is actually a very strong electromagnet and it also has its north and south pole. Why it can be levitated so stably while a permanent magnet cannot?

I don't think that is a good way to think about it. A superconductor expels magnetic fields; if you draw the the field lines you will see that they "bend" around the superconductor and never enters it (if we for the moment neglect he penetration depth, which is usually very small). If the superconductor was behaving like a electromagnet it would also have its own field lines. The permanent magnet is floating on it own field, not on top of a field from superconductor.

Hence, the reason why you can get a stable configuration has to do with the fact that this "expulsion" can create a potential minimum, something that is only possible with diamagnetism,. .

 

[kelvin490]

I don't think that is a good way to think about it. A superconductor expels magnetic fields; if you draw the the field lines you will see that they "bend" around the superconductor and never enters it (if we for the moment neglect he penetration depth, which is usually very small). If the superconductor was behaving like a electromagnet it would also have its own field lines. The permanent magnet is floating on it own field, not on top of a field from superconductor.

Hence, the reason why you can get a stable configuration has to do with the fact that this "expulsion" can create a potential minimum, something that is only possible with diamagnetism,. .

It seems that the expels of magnetic flux is a different mechanism then the use induced current to explain the repulsion. But it also seems this repulsion of field lines is not used in explaining other aspects of magnetism. Are there any ways to formulate it mathematically and also use it to explain, say, repulsion between like poles and opposite poles?

 

[rumborak]

Nah, I think "repulsion" vs "cancellation" are just two different ways of looking at the same thing.

 

[kelvin490]

Field lines from like poles repel each other is a visual way to describe the repulsion in case of magnets, but in magnets there are field lines inside them. It is different from superconductor which doesn't have field lines inside. I wonder whether we can say there is a repulsion between superconductor and magnet just because we see field lines are bend around. And it seems we need a mathematical way to describe the force between them.

 

[rumborak]

Field lines from like poles repel each other is a visual way to describe the repulsion in case of magnets, but in magnets there are field lines inside them. It is different from superconductor which doesn't have field lines inside.

You're not helping yourself in your understanding by treating superconductors as completely new entities that need a new "language" of description. The outside magnetic field *does* penetrate the superconductor, something called the http://en.wikipedia.org/wiki/London_penetration_depth .It is also this surface area in which the currents run that create the canceling magnetic field.

And it seems we need a mathematical way to describe the force between them.

http://en.wikipedia.org/wiki/Maxwell's_equations

 

[kelvin490]

You're not helping yourself in your understanding by treating superconductors as completely new entities that need a new "language" of description. The outside magnetic field *does* penetrate the superconductor, something called the http://en.wikipedia.org/wiki/London_penetration_depth .It is also this surface area in which the currents run that create the canceling magnetic field.
http://en.wikipedia.org/wiki/Maxwell's_equations

I need to clarify what I said previously. The repulsion of lines is a way to describe the repulsion, instead of explain the phenomenon, in situations of both superconductor and magnets. There are always some mechanism behind and the repulsion of field lines is just a result of it. That's why I don't feel comfortable to explain these things in terms of field lines, especially there is no field lines inside superconductor but have field lines in normal magnets. In fact what you said about the induced current previously is already good enough for me to understand the phenomenon, thanks for that.