Building Helmholtz Coils?

Question

Hi,

I'm building a pair of helmholtz coils to do a variety of magnetism-related experiments. I've borrowed an old Avo Douglas coil winder and plan to do a couple of thousand turns on two sections of 50mm or 60mm diameter pipe. Some nylon threaded rod will pass through the middle of each coil, to make the distance between them tweakable, to ensure that the distance between them is exactly equal to the radius of each coil.

I have two questions:

1) Does the physical width of each coil have an effect? That is the width of each layer of the coil. Should this be minimised (e.g. just have five adjacent wires per layer) or does this not have any effect?

2) Is the distance r between the coils the distance between the centrepoint of each coil, or the distance between the closest points on each coil?

Any other comments to do with the practical aspects of making a pair of helmholtz coils and difficulties that may be encountered would be very much appreciated.

With very many thanks,

Froskoy.

Dr. R · Accepted Answer

A Helmholtz coil's design is based on the fact that for two *thin* wire round loops axially separated by 1 radius, the first, second, and third derivatives of B wrt z and r are zero at the center of the assembly. This means you have to move pretty far away from center before B changes significantly. If that is what you want (a fairly uniform B), then you want to approximate a thin wire round loop for each coil. The easiest thing you can do is make the width and height of each wire bundle forming the loop about the same. If you wanted to make absolutely sure the Helmholz coil criterion is satisfied *exactly*, you'd want each winding to be an H. coil itself (separated by radius). This means the assembly will look like an X from the side, but with the center open. Generally, the first solution is what people do. You get a stronger B that way that's still pretty uniform.

Before building anything, I suggest you perform a mathematical exercise to show the above using the Biot Savart Law to find B(z) on axis, and the fact that divergence of B=0 to find the radial derivatives. This will give you the insight needed to figure things like this out for yourself.

Before building anything, I suggest you perform a mathematical exercise to show the above using the Biot Savart Law to find B(z) on axis, and the fact that divergence of B=0 to find the radial derivatives. This will give you the insight needed to figure things like this out for yourself.

Building Helmholtz Coils?

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