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

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Discussion Overview

The discussion revolves around the limits of energy storage in superconductors, exploring theoretical maximums for magnetic fields, the relationship between current and energy storage, and the implications for a fictional narrative. Participants inquire about formulas, critical magnetic fields, and practical examples related to superconducting rings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant questions whether there is a limit to the energy that can be stored in a superconductor and seeks a formula for calculation.
  • Another participant confirms that there is a theoretical maximum for the magnetic field generated by the current.
  • There is a discussion about the critical magnetic field that must not be exceeded for superconductivity to persist in a material.
  • A participant mentions that the critical magnetic field is typically determined experimentally and inquires about typical maximum field strengths.
  • One participant notes that while 40T fields have been achieved in laboratories, the theoretical maximum for magnetic fields is much higher.
  • There is mention of formulas for calculating energy stored in a magnetic field based on inductance and current, but uncertainty remains about their application.
  • A participant expresses confusion about the relationship between magnetic field strength, current, and power, questioning if a specific magnetic field can be directly converted to power values.
  • Another participant seeks clarification on how to determine the size of a superconducting ring that would generate a desired magnetic field strength.

Areas of Agreement / Disagreement

Participants generally agree that there are theoretical limits and critical values related to superconductors and magnetic fields, but there is no consensus on specific values or formulas. The discussion remains unresolved regarding the practical application of these concepts.

Contextual Notes

Participants express uncertainty about the specific formulas and calculations related to energy storage in superconductors, as well as the definitions and dependencies of terms like inductance and power.

Who May Find This Useful

This discussion may be useful for individuals interested in superconductivity, magnetic fields, and their applications in theoretical or fictional contexts, particularly in the realms of physics and engineering.

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

yes
 
That being the critical magnetic field before superconductivity ceases in that material?
 
of course
 
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?
 
Just checking back on this last question, any ideas anyone?
 

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