Lorentz force on superconducting wire?

[Terawatt]

Hello,

I've been trying to puzzle this one out and even the mighty internet has not been particularly helpful, so here goes:

Say you have a current carrying copper wire perpendicular to a magnetic field. Let's give some values for clarity: the length of the wire is 1m, the current is 3A, and the magnetic field is 2T. The Lorentz (Laplace) force on that wire should be F = Il x B. In our case, F = 3A * 1m * 2T for a total of 6N of force in a direction given by my favorite, the right hand rule.

Ok, that makes sense to me. Now, say instead of a copper wire, you substitute in a superconducting wire (operating in its superconducting regime) with the same values. Will there still be a 6N force on that wire? I am confused because, as I understand it, the Meissner effect expels the magnetic field from the interior of a superconductor. So, is the current in the wire still feeling the magnetic field or is it now "immune" to it? Is there no force on the superconducting wire, a reduced force, or still the same 6N force? Relatedly, does the proximity to the critical temperature and critical current density have any affect on the answer?

I'd appreciate any helpful insight, particularly if you could explain in detail why (or why not) the superconducting wire has a force on it.

Regards,
Terawatt

 

[falcon32]

Terrawatt, I'm going to attempt to answer your question. :)
In a superconductor, the current flowing through the wire exists on the skin only. The field of this skin current is self-cancelling within the wire (the Meissner effect), but it exists outside of it. Therefore, since the current on the wire's surface is exposed to any applied magnetic field, it should still react, since the Lorentz force is the reaction of our moving, charged electrons with respect to this field.

 

[Terawatt]

Great, thank you for the response falcon32. I was getting confused by what was happening inside the wire, but it makes sense that there would still be a force if the current is subject to an external magnetic field on the surface of the wire.

So, I suppose this has a follow up question. If one were to apply current to a superconducting wire in the presence of an external magnetic field, one would get a force. Let's say the wire is fixed in place. If one draws a control volume around the wire (excluding energy going into making the magnetic field and keeping the superconductor cool), it appears that no energy is consumed to apply a force to the wire, correct? No energy is lost in the wire. Current flows in, the same current flows out. Magnetic field flows into your control volume, the same field flows out. Now, if we unfixed the wire so that it could move, there should be energy transfer by E=F*d=(Il x B)*d. Where is that energy coming from that goes into the moving wire? Is the magnetic field altered by the moving wire in such a way that it would take more energy to maintain that field?

Terawatt

 

[falcon32]

"it appears that no energy is consumed to apply a force to the wire"...

Keyboard scientists can only go so far. :) I suspect if you physically conduct the experiment with a superconductor -- if you are lucky enough to know where to get one -- you will find that this will be the case:

Your magnetic field is performing work on the electrons in your superconducting wire, forcing them, and thus the wire, to physically move. Therefore, whatever generates your external field has expended some energy in this work. The energy required to move a wire is very small, but if you had instruments sensitive enough to measure it at the EM generator, you would find that a tiny amount is missing --- the amount required to move your wire.

 

[f95toli]

The energy would come from the generator.

Also, the fact that the wire is superconducting does not really change anything in this case. A wire is i these situation always -to a first approximation- a 1 dimensional object meaning how the current flows in the wire itself does not change anything.

 

[Phrak]

Now, if we unfixed the wire so that it could move, there should be energy transfer by E=F*d=(Il x B)*d. Where is that energy coming from that goes into the moving wire? Is the magnetic field altered by the moving wire in such a way that it would take more energy to maintain that field?

Assume the wire moves under an adverse force, so that E is positive, and that it moves a distance d in time t. The power required is P=E/t. The superconductor, or any conductor ignoring small resistance, will have a potential develop across the length lying within the magnetic field such that P=VI. This assumes constant current.

If V is constrained to be zero, such as the case of a closed superconducting loop, the current will increase such that E=(1/2)IL^2, where L is the inductance of the loop.

I hope this keyboard scientist hasn't caused falcon32 any anguish with this keyboard answer.

 

[falcon32]

Assume the wire moves under an adverse force, so that E is positive, and that it moves a distance d in time t. The power required is P=E/t. The superconductor, or any conductor ignoring small resistance, will have a potential develop across the length lying within the magnetic field such that P=VI. This assumes constant current.

If V is constrained to be zero, such as the case of a closed superconducting loop, the current will increase such that E=(1/2)IL^2, where L is the inductance of the loop.

I hope this keyboard scientist hasn't caused falcon32 any anguish with this keyboard answer.

LOL, well the second question by Terrawatts was "where is the energy coming from", and a few of us told him, from the generator providing the external electromagnetic field.

I personally find it fascinating that, since there is no resistance in a superconductor, there is therefore no voltage drop. Means that a superconductor loop (as has been observed) that has no power source, if it were moved at right angles through an EM field, and then the field were turned off, would keep the current going for years. Some say forever! A very expensive battery!

 

[Phrak]

I personally find it fascinating that, since there is no resistance in a superconductor, there is therefore no voltage drop.

No, this is not in general true. Read my post you found so amusing Again.

 

[falcon32]

No, this is not in general true. Read my post you found so amusing Again.

"great efficiency achieved with great ease. In fact, when you have a superconducting current going, it can keep on going and going and going – long after you unplug the machine"

--Quote courtesy of Florida State University.

http://www.magnet.fsu.edu/education/tutorials/magnetacademy/superconductivity101/

 

[Phrak]

"great efficiency achieved with great ease. In fact, when you have a superconducting current going, it can keep on going and going and going – long after you unplug the machine"

--Quote courtesy of Florida State University.

http://www.magnet.fsu.edu/education/tutorials/magnetacademy/superconductivity101/

Cute article for laymen. An energy storage medium is not a energy source. However, if you know anyone willing to think otherwise, please direct them to myself, care of this forum, so I can fleece them of their own ill got dollars and life's savings.

 

[falcon32]

Who thinks its an energy source? Energy cannot be created or destroyed, merely transformed. The only energy you would get out of a shorted superconductor is exactly the amount you would put in. You puzzle me...

 

[Phrak]

Who thinks its an energy source? Energy cannot be created or destroyed, merely transformed. The only energy you would get out of a shorted superconductor is exactly the amount you would put in. You puzzle me...

Then what is your point? You're linked article never hints at this. What was your intent in posting it?

 

[Terawatt]

Thank you for all the responses. Now, please correct me if I am wrong, but here is what I am gathering...

In the case of no wire motion: If the superconducting wire is infused with a current, and the wire shorted into a loop, it will keep that current. If that wire is placed in an external magnetic field and fixed in place, there should be a force on that wire, but since the wire is not moving, no energy is lost and the current will keep flowing. There is a constant force on the wire. No energy needs to be added to the system to keep the force applied to the wire.

In the case of wire motion: If the superconducting wire is infused with a current, and the wire shorted into a loop, it will keep that current. If that wire is placed in an external magnetic field and not fixed in place, there should be a force on that wire which causes it to move. Energy is transferred from the source of the magnetic field into the wire's motion. Energy must be added to this system to keep the wire in motion.

Is this anywhere close to correct or am I inferring incorrectly?

Thanks,
Terawatt

 

[falcon32]

Then what is your point? You're linked article never hints at this. What was your intent in posting it?

Ah, we misunderstood each other. My point was to show that once energy is added to a shorted superconductor, it retains this energy in the form of an indefinite current until you remove it by shuttling this stored energy into some kind of a circuit, thus using it up.
Because the current can persist for years (some experts say millions), it therefore follows that there cannot be any resistance in the superconductor.
We know that resistance consumes energy, creating heat and using up part of the current. if resistance existed in superconductors, then in our specific scenario, current would quickly decay to zero, which is not the observed case.

 

[cragar]

No, this is not in general true. Read my post you found so amusing Again.

So are you saying that we can have an E field inside the superconductor.

 

[Phrak]

Ah, we misunderstood each other. My point was to show that once energy is added to a shorted superconductor, it retains this energy in the form of an indefinite current until you remove it by shuttling this stored energy into some kind of a circuit, thus using it up.
Because the current can persist for years (some experts say millions), it therefore follows that there cannot be any resistance in the superconductor.
We know that resistance consumes energy, creating heat and using up part of the current. if resistance existed in superconductors, then in our specific scenario, current would quickly decay to zero, which is not the observed case.

It sounds good to me. I'd add that changing the quantity of magnetic flux passing through the loop will also change the stored energy.