Why don't superconductors emit a lot of heat?

[osnarf]

Hi everyone, just a quick question.

I just heard someone say a superconducting electromagnet does not produce heat, which I find very strange, since it seems that, since rate of heat energy being dissipated = voltage^2/resistance. Taking the limit as resistance goes to 0, with voltage held constant, power approaches infinity. I remember reading that resistance is not exactly zero, but it's very close, so it stands to reason that this low of a resistance should produce a ton of heat. Hence, confusion.

Thanks for your help.

[Jiggy-Ninja]

I am not intimately familiar with superconducting magnet technology, but I can say this: super conductors have zero electrical resistance. Not a small amount, not practically zero, but exactly zero. It's some weird quantum mechanical effect that I can't remember the name of, but there is literally 0 ohms resistance in a superconducting wire. That's why they are such a huge deal.

If your intuition can't grasp how it can be exactly zero, don't worry. Quantum mechanics is beyond any form of human intuition.

[vk6kro]

Hi everyone, just a quick question.

I just heard someone say a superconducting electromagnet does not produce heat, which I find very strange, since it seems that, since rate of heat energy being dissipated = voltage^2/resistance. Taking the limit as resistance goes to 0, with voltage held constant, power approaches infinity. I remember reading that resistance is not exactly zero, but it's very close, so it stands to reason that this low of a resistance should produce a ton of heat. Hence, confusion.

Thanks for your help.

The heat produced is also zero because you can't produce a voltage across zero resistance without infinite current.

A better formula would be Power = I2 times R
So whatever current you do send through the superconductor is multiplied by zero to give you zero power.

[MATLABdude]

This comes up on this forum every so often, but the very definition of a superconductor is that it has zero resistance. If you get a current circulating around in one (pumping via Lenz's Law) it'll keep on going forever (or until the superconductor warms up, stops becoming a superconductor, and blows up / melts down instead):
http://www.physicsforums.com/showthread.php?t=250863

[osnarf]

Okay that makes sense, I thought it was near zero, not exactly. Thanks for clearing it up.