# Is there a limit to the amount of energy stored in a superconductor?

1. Sep 9, 2010

### Barwick

I'm curious, neglecting all the worries about temperature, etc (assume those conditions can be met)...

Is there a limit to the amount of energy that can be stored in a superconductor? Is there a formula to calculate it? What causes this limit, etc?

Is there a massive field generated by the current? Is there a theoretical maximum for a magnetic field generated by the current?

Is there a theoretical maximum "saturation" limit where no more electrons can be packed onto the surface or within the structure (do they only reside on the surface in a superconductor? am I way off my rocker on this part? I dunno...) Is the amount of energy stored based on the eV of each electron? I'm really clueless on this as you can tell, I'm trying to figure it out, and the insanely formula-heavy papers I've tried to read haven't helped a whole lot to get the basics.

Basically, I'm assuming a ring shaped superconductor, just to throw out some numbers, let's say it's 5cm diameter, and the "wire" is 1mm thick. Is this limited to a certain number? What if we doubled the diameter and kept the same thickness of the "wire"? What if we made the "wire" 1cm thick instead of 1mm, and kept the same diameter of the ring?

2. Sep 9, 2010

### granpa

Is there a theoretical maximum for a magnetic field generated by the current?

yes

3. Sep 9, 2010

### Barwick

That being the critical magnetic field before superconductivity ceases in that material?

4. Sep 9, 2010

of course

5. Sep 9, 2010

### Barwick

Hm... near as I can tell the critical magnetic field is only experimentally determined for each superconductor. What is a typical value for the maximum field strength?

I know people have created 40T fields in laboratories, and that's about the most that has been sustained on earth. Though the maximum theoretical value for a magnetic field is an absurdly high number.

I know there's formulas to calculate the energy stored in a magnetic field, and it's based on the inductance and current in it. For the life of me I can't figure this out.

Basically, I'm writing a fictional story that is somewhat based in reality. I don't want to say something that is so completely out in left field that the reader is going to say "this is stupid".

There is no direct conversion of say a 40T magnetic field to a value of power. Tesla being a measure of inductance, and Watts being a measure of power.

So, if I said I had a 40T magnetic field that generated a current of (something) over a length of area of (something), that would mean I have X watts of power stored in that magnetic field.

Is that correct? I'm not thinking it is, but I really have nowhere else to go on this... But if it was, then I have to figure out what size ring would generate a field of whatever current over whatever length?

6. Sep 13, 2010

### Barwick

Just checking back on this last question, any ideas anyone?