## Does the width of a superconducting wire matter?

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Oort
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### Does the width of a superconducting wire matter?

I figured it wouldn't, but would a large current make a difference?

run.dll
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### Re: Does the width of a superconducting wire matter?

Matter for what? Current-carrying capacity?

If by width you mean diameter, then the effect of increasing the diameter is to decrease the current density, defined as the current per unit cross sectional area (J/m^2).

If the wire suddenly becomes non-conducting, the normal resistance of a wire is inversely proportional to the cross-sectional area and therefore inversely proportional to the square of the diameter, so you are less likely to get excessive joule heating.
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ThomasS
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### Re: Does the width of a superconducting wire matter?

Superconductors have a current limit. Run too much current through them and they stop superconducting. Before that point there is of course no heating, etc. Similarly, they exclude magnetic field perfectly, until the field density gets high enough and then they don't. The details of the failure depend on whether it is type I or type II.

Oort
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### Re: Does the width of a superconducting wire matter?

I meant how would it affect resistance.

Thanks for the answers. So now I'm wondering, how is current limit determined and is it affected by width (diameter)?

ThomasS
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### Re: Does the width of a superconducting wire matter?

Oort wrote:I meant how would it affect resistance.

Thanks for the answers. So now I'm wondering, how is current limit determined and is it affected by width (diameter)?

They have no resistance ofc, that is the point. But the current limitation is the equivalent. I haven't specificaly studied superconductors, but I'm pretty sure that the current limitation is proportional to cross section, just as you would expect. There is a basic mention of the phenomenon here, but the documents I've googled that are most likely to really answer your question appear to be meant for an advanced audience.

JWalker
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### Re: Does the width of a superconducting wire matter?

It does matter, especially if the width of the superconductor is very small in one direction (ie and extremely flat wire). There are many interesting phenomena in what are called low dimensional superconductors, but you'll most likely be unable to find any literature on them that isn't at an extremely advanced level.

Tass
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### Re: Does the width of a superconducting wire matter?

Remember that all current in a superconductor runs on the surface, that may intuitively explain why flat ribbons are good. I am not entirely sure, but I would guess current capacity roughly scales with surface area.

SpitValve
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### Re: Does the width of a superconducting wire matter?

Tass wrote:Remember that all current in a superconductor runs on the surface, that may intuitively explain why flat ribbons are good.

I thought it was because the most useful superconductors are made from brittle ceramics, and it's easier to grow them in layers than to mould them into wires...

scienceandreason
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### Re: Does the width of a superconducting wire matter?

It's actually a critical current density that matters. Once the wire has a current density beyond it's limit the superconducting state is no longer stable and it will collapse. Therefore, the thicker the wire the more current you can carry for a given supercurrent.

scienceandreason
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### Re: Does the width of a superconducting wire matter?

SpitValve wrote:
Tass wrote:Remember that all current in a superconductor runs on the surface, that may intuitively explain why flat ribbons are good.

I thought it was because the most useful superconductors are made from brittle ceramics, and it's easier to grow them in layers than to mould them into wires...

You are mostly correct. All high-tc superconductors are ceramics and very hard to grow in any great quantity. usually what is done is YBCO polycrystals (high-tc) are mounted with another conventional superconductor to make the wire. This relies on a proximity effect between the two where the YBCO film raises the critical temperature of the conventional material (which is usually Al or a binary alloy).

everyonemines
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### Re: Does the width of a superconducting wire matter?

Tass wrote:Remember that all current in a superconductor runs on the surface, that may intuitively explain why flat ribbons are good. I am not entirely sure, but I would guess current capacity roughly scales with surface area.

No it doesn't. That's the case with the current created in response to an external magnetic field, though, to some extent.

Superconductors have a per-cross section critical current, but that decreases with magnetic field, which increases with current.

Tass
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### Re: Does the width of a superconducting wire matter?

everyonemines wrote:No it doesn't. That's the case with the current created in response to an external magnetic field, though, to some extent.

Superconductors have a per-cross section critical current, but that decreases with magnetic field, which increases with current.

It is certainly true for type I superconductors (yes I know most commercially used are type II) Current means a B field with curl, which means that is cannot be zero all around the current, which means that any current must be adjacent to something nonsuperconducting.

everyonemines
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### Re: Does the width of a superconducting wire matter?

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### Re: Does the width of a superconducting wire matter?

Oort wrote:I figured it wouldn't, but would a large current make a difference?

Depends on what you mean by mattering. Superconductivity as a phenomena does not depend on the dimensions of the material, but dimension does put a cap on how much current you can pass through it. You can still power a medium sized city with a fairly small wire (I did some calculations on that once, and I think the required radius of the wire was around a couple of decimeters ~ 1 ft to centimeters~inches, depending on what material you use.)
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### Re: Does the width of a superconducting wire matter?

Meteorswarm wrote:Would a hollow wire (roughly) double the capacity, not affect it, or lower it?

Lower it.

There is a critical current density. If you have a fixed current going through a wire and you remove some of the cross sectional area, the current density goes up.

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### Re: Does the width of a superconducting wire matter?

Meteorswarm wrote:Would a hollow wire (roughly) double the capacity, not affect it, or lower it?

Lower it.

There is a critical current density. If you have a fixed current going through a wire and you remove some of the cross sectional area, the current density goes up.