# Superconducting magnet with HTS wire

• MagnetDude
In summary, a flat spiral coil with a width and height will produce a magnetic field that is approximately PxNxI/L. This field can be approximated using a single turn with average radius multiplied by spiral current and number of turns. To calculate the tesla strength of the magnetic field, you will need to know the inner and outer radius of the coil, as well as the number of turns.

#### MagnetDude

Hey guys, I am building a superconducting magnet. The wire I have is extremely thin, and is flat. To put it more into perceptive it has a width and height. When I wind it into a magnet, it is more like a disk coil, or racetrack coil. Because it has a different geometry than most other electromagnets, what equation would I use to calculate its magnetic field?

Most equations I have seen are a little something like this.

p=permeability
I=current
N=Number of turns
L=length of turn

The ones I have seen are PxNxI/L.

That goes for a solenoid mainly. The length of the coil I will make, if it were to be a disk, would be the Thickness of the wire times the number of turns, its width would have nothing relevant enough do with the calculation I would assume. After I find the turn density, what do I do? It is going to be a really weird magnet.

In most cases you end up having to use numerical methods, e.g. FEM using something like COMSOL.
Analytical methods rarely work unless you have a very simple geometry (e.g. a long solenoid(

The coil I think you are describing is called a “pancake” or a “flat spiral” coil.
The question as to which model to use really depends on the inner to outer radius ratio.

A simple magnetic model is a flat conductive disk with inner and outer radii that has a sheet current circulating, the sheet current is Nturns times the spiral current. That may give you a simple analytic solution.

A first approximation of the field could be that of a single turn with the average radius, multiplied by spiral current and number of turns.

f95toli said:
In most cases you end up having to use numerical methods, e.g. FEM using something like COMSOL.
Analytical methods rarely work unless you have a very simple geometry (e.g. a long solenoid(

F95toli: This is not a long solenoid though, this is a flat solenoid. To give you more of a perceptive of this wire, here is a link to the

Baluncore said:
The coil I think you are describing is called a “pancake” or a “flat spiral” coil.
The question as to which model to use really depends on the inner to outer radius ratio.

A simple magnetic model is a flat conductive disk with inner and outer radii that has a sheet current circulating, the sheet current is Nturns times the spiral current. That may give you a simple analytic solution.

A first approximation of the field could be that of a single turn with the average radius, multiplied by spiral current and number of turns.

I just spent about 30 minutes googling what you suggested, and that you were stating seemed to be right, but all the equations I am finding are for inductance. I am not finding anything that gives me the tesla strength of the magnetic field.

There are many users of pancake coils for SC magnets.
Google 'magnetic field of pancake coil' or 'magnetic field of spiral coil' and you will get examples of flat spiral design.

Do you need axial field only ?
http://spectronet.de/portals/visqua/story_docs/vortraege_2009/090520_measurement/090520_tag1/090520_03_andris.pdf

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Baluncore said:
There are many users of pancake coils for SC magnets.
Google 'magnetic field of pancake coil' or 'magnetic field of spiral coil' and you will get examples of flat spiral design.