Constructing a Tri-Axial Square Helmholz Coil

In summary, this student is trying to build a tri-axial square helmholtz coil setup. He has been researching for days and is having trouble figuring out the correct dimensions, turns, necessary wire thickness, and current. He has been using the Biot-Savart law to calculate the magnetic fields of the coils. He found that the B-field (in Gauss) produced at the midway point between a pair of square coils is (.001629)*I*N/L where I is the current, N is the number of turns, and L is the length of a side of a coil. He needs at least 14 gauge copper wire for this setup.
  • #1
rushingwind
3
0

Homework Statement


I'm a summer REU student tasked with building a tri-axial square helmholtz coil setup. My frame will be made of aluminum while the wire used will be copper. I've been researching for days, having actually never studied these coils before, and I'm having serious trouble figuring out the correct dimensions, turns, necessary wire thickness, and current.

The center of the field will contain a MOT. I'm looking to cancel out slightly more than 1 gauss. Presently, I don't quite understand how to apply Gauss's Law (or if I'm doing it correctly/incorrectly), as I've only taken Introductory Physics (I have, however, taken Calculus, but not Calc II).

The Attempt at a Solution



So far, this is the setup I've been able to come up with: (I've edited this after finally being able to see my workspace). I'm very limited in space, so the sides of each square set must be 18in (about .46m), 16in (about .41m), and 14in (about .36m). That brings my calculations for spacing between pairs to .25m, .2m, and .19m, respectively.

Running 2A of current through each coil (can't go below 1A, or above 5A), these are the number of turns I calculated:

18in/.46m -- 15 turns
16in/.41m -- 13 turns
14in/.36m -- 12 turns

I need to cancel out slightly more than 1 gauss at the center of this tri-axial configuration, and my math shows me that it does... If I'm doing this right. I've also calculated that I need at least 14 gauge copper wire for this setup.Disclaimer: I appreciate any pointers because I actually have no idea what I'm doing, even after days of research. I don't know if my work is on the right track or completely off, as this is a little beyond my current level of physics education! Any help (or pointers in the right direction!) would be greatly appreciated.

Thank you in advance.
 
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  • #2
Gauss' law isn't relevant here. The magnetic fields of the coils can be calculated using the Biot-Savart law. Using that law I found an expression for the field produced at the midway point between a pair of square coils if the distance between the coils is the optimal distance of .5445 L, where L is the length of a side of a coil. I find that the B-field (in Gauss) produced at that point is

B = (.001629)*I*N/L where I is the current, N is the number of turns, and L is the length of a side of a coil.

This seems to agree fairly closely with your figures.

The currents in the two coils should be in the same direction.

The direction of the field will be along the axis of the pair of coils. Thus, with three pairs of coils whose axes are mutually perpendicular, you can produce fields in any direction at the midpoint by independently adjusting the currents in the 3 pairs of coils.

Here's a document that contains a picture of a tri-axial square helmholtz coil
http://www.laboratorio.elettrofisico.com/pdf/Misura/mis_01_helmholtz_coils.pdf [Broken]
 
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  • #3
Thank you so much, TSny. I was having trouble trying to apply Gauss' Law... no wonder! I feel more confident about the numbers I came up with now. Thank you so much for the link to the document, and your guidance.
 
  • #4
Helmholtz coils are designed to produce a uniform magnetic field at the center, specifically one in which the quadratic change in field along the axis (i.e., the second derivative) is zero. The spacings of your first and third coils are correct to produce the Helmholtz condition, but the second spacing is inconsistent with its coil dimension. Here is a reference that may be helpful:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&sqi=2&ved=0CE8QFjAC&url=http%3A%2F%2Fdigitalcommons.unl.edu%2Fcgi%2Fviewcontent.cgi%3Farticle%3D1043%26context%3Dphysicsrudd&ei=yyLpT5SFJo2K8QSk8dGCDg&usg=AFQjCNGp8OwoTtpXteHoXfO7WiNyQoXTMg
A Google search on square Helmholtz coils will produce many others.
 
  • #5
marcusl said:

That's an interesting reference. I wasn't aware that increasing the separation beyond the "Helmholtz distance" of .5445L increases the distance of uniformity of the field along the axis.

Thanks.
 
  • #6
Thank you so much everyone. I really appreciate the references and the help. I'm going to start building two of the coils tomorrow in the shop room. You guys are a lifesaver! :)
 

1. What is a Tri-Axial Square Helmholz Coil?

A Tri-Axial Square Helmholz Coil is a device used in experimental setups to generate a uniform magnetic field in three dimensions. It consists of three pairs of square coils, each pair oriented in a different axis, arranged in such a way that the magnetic fields they produce overlap and cancel out at the center of the coil.

2. What materials are needed to construct a Tri-Axial Square Helmholz Coil?

The materials needed to construct a Tri-Axial Square Helmholz Coil include copper wire, a power supply, a wooden frame, a drill, and wire cutters. Optional materials include a multimeter and a soldering iron for more precise measurements and connections.

3. What are the steps to construct a Tri-Axial Square Helmholz Coil?

The steps to construct a Tri-Axial Square Helmholz Coil are as follows:

1. Measure and cut the wooden frame to the desired size.

2. Drill holes in the wooden frame to thread the copper wire through.

3. Wind the copper wire around each square coil, making sure to have an equal number of turns for each coil.

4. Thread the wire through the holes in the frame, connecting each coil in series.

5. Connect the power supply to the ends of the wire, ensuring that the current flows in the same direction for each coil.

6. Use a multimeter to measure the magnetic field strength at the center of the coil.

4. What are the benefits of using a Tri-Axial Square Helmholz Coil?

The benefits of using a Tri-Axial Square Helmholz Coil include:

1. The ability to generate a uniform magnetic field in three dimensions, making it ideal for experiments and research in physics and engineering.

2. The use of square coils allows for a more compact design compared to traditional circular Helmholz coils, saving space in experimental setups.

3. The overlapping and cancelling of magnetic fields at the center of the coil reduces magnetic interference and increases accuracy in experiments.

5. How can I ensure the accuracy of my Tri-Axial Square Helmholz Coil?

To ensure the accuracy of your Tri-Axial Square Helmholz Coil, you can:

1. Use a multimeter to measure the magnetic field strength at the center of the coil.

2. Make sure to wind an equal number of turns for each coil and connect them in series.

3. Use a power supply with stable and precise current output.

4. Keep the wooden frame of the coil stable and secure to prevent any movement or changes in the magnetic field.

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