# User:Brian P. Josey/Notebook/2010/03/15

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## Magnetic Yoke

This is probably the best place to buy the cylindrical magnets, K&J Magnets. Their magnets are reasonably priced, and have various sizes. All magnets are neodymium, and magnetized along the axis. The cone magnets that I have have a base diameter of 1/2", and I would like to use cylinders that are about the same size so that there is not unnecessary overlap. So using cylinders with either a 3/8" or 1/2" diameter should be good. I am still trying to find some horseshoe, or other magnets that I like for the bends. I need to know the shape and dimensions of the bends before I can design the rest of the yoke.

Steve Koch 00:21, 17 March 2010 (EDT): Did you ever investigate the difference between using iron for the yoke (which we can bend) versus neodymium? Or is that what you're working towards. It does seem like neodymium would work better, but given how poor my intuition is, it wouldn't be surprising if I'm wrong that it's a big effect. Looked like from today that you're very close to being able to investigate this with FEMM directly, which is great! You're learning that software very quickly!

## Derivatives of Magnetic Field

The force on a magnetic moment in a magnetic field is given by:

${\displaystyle {\vec {F}}={\vec {m}}\cdot (\nabla {\vec {B}})}$

Where F is the force, m is the magnetic dipole and B is the magnetic field. Because the force depends on the gradient of the magnetic field, I can take the derivative of the field along a line connecting two points that I am interested in, and it serves as a decent approximation for the general force:

### Magnetostatics Tutorial

Here is the magnetic field strength from the tutorial I did last Wednesday. The magnetic field as a function of length is on the left, and as expected, it is a parabolic with the greatest field in the center of the length. The derivative is on the right and is a little more interesting. Unfortunately, the derivative is not smooth. I am not a hundred percent sure what the cause of this is, I could have had either too large of a mesh size, or too few points, I used 300, for the graph.

Steve Koch 00:22, 17 March 2010 (EDT): I struggled a lot with the non-smooth derivative. I came up with a LabVIEW smoothing algorithm for the Sandia work. This is likely similar to what Larry and I had to do with the image tracking smoothing. So we should definitely talk about those algorithms, it would be very good for you to learn.
Brian P. Josey 11:14, 17 March 2010 (EDT) I would actually really like to learn that algorithm, it would help out a lot, and if I can develop one in MATLAB, I can take it home with me to use.

### Side of Cone to Flat Surface

These two are from the model Koch did of the magnetic yoke that we have now. The field is on the left, and the derivative is on the right. For both of them, the cone is on the left side of the graph , and the flat surface is on the right. The field is not that surprising, the yoke was designed to have the greatest field on the cone, and the field lines are directed around the yoke to the flat side. The jump though is a little different, and looking at the data, the field jumps from 1.59688165e-001 to 1.82864671e-001 T in 2.45e-3 inches. Coding it out removes the anomaly, but I'm leaving a note to look at it and fix it tomorrow. Just in case there is some deeper issue with it.

### Tip of Cone to Center of Flat Surface

I had two positions in the model to work with. One from halfway up the cone, and the other from the tip of the cone. These two are the field, left, and derivative, right, from the tip of the cone to the center of the flat surface across the gap. Here it is really pronounced how strong the field is near the tip, left side in both pictures. Up too about 0.025 inches, there would be a very strong magnetic force on any magnetic moment, and outside of that, the force is much weaker. This is about four times the thickness of the cover glass that we use, 0.17mm or 0.00669 inches, from the manufacturer. If we keep the magnet close enough to the ferritin, less than the 0.025 inches, then there will be a greater amount of force than farther away. This is also probably why I ran into some trouble with my earlier experiments. There was simply too much of a gap between the tip of the magnet and the ferritin.

Steve Koch 00:26, 17 March 2010 (EDT): Very nice conclusion and I really like how you're using the modeling to compare with real-life examples (such as coverglass thickness) -- that is exactly why the modeling is useful, good work!
Steve Koch 00:27, 17 March 2010 (EDT): I'm trying to find my old summaries of this magnet, along with hall probe measurements. If I can't easily find that, I'll at least try to show you the raw data to see if you agree. What current density in the copper were you using? That's useful information. I should show you how to put files in the "web pub" so you could link to exact modeling files. Or possibly use Google Docs (which supposedly can accept any file type now?).
Brian P. Josey 11:39, 17 March 2010 (EDT) I am just using the old model you made back at Sandia, the "copper top" has a current density of -9.69 MA/m2. The copper is wrapped around the iron core, which has no current density of its own.

#### Links to Steve's old files

Steve Koch 01:09, 17 March 2010 (EDT): I found some files and moved them to the webpub directory. You can find them here: http://kochlab.org/files/Magnets,%20MEMS,%20etc/Cone,%20Flat%20Magnet%20Modeling%20(Magnet%202)

• The Word document at the end of page 1 shows a graph of the FEMM predictions and two sets of hall probe measurements. The current is 10Amps, which I think maybe corresponds to 9.79 amps per whatever in the modeling software.
• Also, here is the FEMM data, I think: /FEMM results, 10 Amps
Brian P. Josey 11:39, 17 March 2010 (EDT) The data looks great, it matches what I was getting perfectly. After I create the neodymium yoke model, I will use this as a comparison.

## For Tomorrow

• Magnetic moments of the constituents of ferritin
• Gradient of the magnetic field in FEMM
• Apply both to above calculations
• Design yoke
• find bends you like