Power of superconductor magnets

[CaptainPanic]

Just out of curiosity, how do you go about calculating how much electric power is consumed by an electromagnet made of superconducting material? Since the resistance is zero, it would suggest that the current can be (nearly?) infinite.

 

Wikipedia tells me that the only power consumed in a DC electromagnet is due to the ohmic resistance.

Another wikipedia site tells me that superconducting magnets can maintain a current with no voltage applied whatsoever, a property which is used in MRI machines.

 

But what if a magnet does work? What if a charged particle comes near, and the magnetic force acts on it? Shouldn't that alter the current in the superconducting magnet through induction? But getting the current back up to the old level would then again require no power?

 

And is there a practical upper limit to how much current you can push through a superconducting magnet? (Is there even a theoretical limit?)

[Observer B]

Perhaps you noticed the wikipedia article on Superconductor referenced the Meissner effect, which is "the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state" (A material transitions to the superconducting state when it is cooled below a certain critical temperature). Induction doesnt take place in this situation as it would in any other. The article continues; "In a weak applied field, a superconductor "expels" nearly all magnetic flux. It does this by setting up electric currents near its surface. The magnetic field of these surface currents cancels the applied magnetic field". If you search superconductor in google images you see a lot of this:

This is a picture of a magnet hovering over a piece of superconducting material (which has been cooled below its critical temperature; notice the liquid nitrogen evaporating). The magnet hovers because of the Meissner effect. Magnetic flux from the hovering magnet is expelled from the superconducting material below it. Generally induction is thought of as an electromagnetic field influencing the electromagnetic properties of a material, but in this case the material has zero resistance. The magnetic field lines are directly responsible for the electrical currents in the superconducting material which balance them out.

So in a way you could say yes, the magnet alters the current in the superconductor, but it generates a current which induces a balancing magnetic field. Power is out of the picture because there is no resistance; the stationary magnetic field is enough to generate a current.

I dont think there is a theoretical limit to the amount of current that can be put through a superconducting material, but i also couldnt tell you what a practical limit might be. I think I sill have some information on possible explanations for practical limits, but I'd have to dig it out from my school stuff. Superconductivity has been studied for almost 100 years now but we're still missing a dynamical theory to explain the phenomenon. If you figure it out, you could probably get a nobel prize.

 

Hope this answered at least some of your questions, sorry I couldnt be more specific.

 

I wanted to post this to you sooner but I was accidentally banned because someone thought I posted spam...

Seeing as this is only my third post and my first one was in the welcome thing, Im guessing it had to do with one of my posts about opencourseware. Its rather interesting how quick they are around here to block someone out completely with no explanation or any way to contact administrators. I had to reply to the welcome email.

[Cap'n Refsmmat]

And is there a practical upper limit to how much current you can push through a superconducting magnet? (Is there even a theoretical limit?)

At some point (the critical field), the high magnetic field causes the superconductor to no longer be superconducting. The other practical concern is quenching; if the magnet warms up and gets a resistance, the huge current starts melting things.

[DrRocket]

The other practical concern is quenching; if the magnet warms up and gets a resistance, the huge current starts melting things.

 

Which makes it difficult to maintain the low temperatures necessary to maintain a superconducting state.

[John Cuthber]

I have a magnet holding a piece of paper on the door of my fridge.

Nothing moves so no work is done. If I had the magnet on the inside of a very cold fridge, I could use a superconducting coil instead of the magnet.

 

There is no need for any power to be dissipated in either case.

 

If an electron or other charged particle were to pass near this magnet it would experience a force but the force is in a direction at right angles to the motion so no work is done and no power is needed.

(it's like the fact that I can roll a 1 ton car on a flat road, in principle, without taking any power. In practice there's a bit of friction. It's only if I want to go up hill that I need to do a lot of work.)

 

The only power needed by a superconducting magnet is the power that drives the fridge.

 

The stored energy in a current carrying inductor is 1/2 L I^2

So, since the inductance (L) is not zero, the current has to be finite because the stored energy can't be infinite, but it can be quite large.

[Observer B]

The other practical concern is quenching; if the magnet warms up and gets a resistance, the huge current starts melting things.

 

Ah yes, quenching... thats the word I was looking for. Even a little quenching can completely ruin a superconducting material by altering its magnetic properties. This is a huge concern for big research facilities or any organization that uses superconductors.