# Construction for a homogeneous field using permanent magnets

Please let me describe what I am trying to achieve and I will pose my question in the end.

I am trying to design a small chamber which can have a uniform magnetic field inside. I want to see if a design using permanent block magnets is feasible in terms of cost and construction. The volume inside the chamber is approximately 13cm x 13cm x 13cm.

I am thinking of using an iron or steel yoke as shown in the picture below. I got the idea from this article in supermagnete.de.

The picture below shows a top-view of my current design, where the green is a block magnet and the gray is iron or steel:

To reduce construction costs, I am planning to laser-cut many pieces and stack them as shown below:

This is an experimental prototype design, in which I care more about the field homogeneity rather than the field strength itself.

My question is the following: Would such a construction produce a fairly homogeneous field? I am concerned that the size of the magnet and the geometry of certain areas of the sheet matter, but I am not entirely sure how to design for them.

Given the technical details of the magnets, for example this datasheet, how can I estimate the field strength inside the chamber?

With that in mind, is there any free software that can easily simulate the fields in such a geometry? I could use that to see the effect of different geometries and magnets.

Thanks for all the help in advance!

• Do you need a permanent magnet? A Helmholtz coil has a very uniform field inside it and would probably be easier. Commented Jul 25, 2020 at 18:27
• I have tried Helmholtz coils, but for my application I need a lot of turns and it becomes expensive and difficult to make without a coil winding machine. It is not off the table, I was just considering permanent magnets as an alternative. Commented Jul 25, 2020 at 18:38
• @tony31 How about making a coil winding semi-machine yourself? HAM operators have been building them for decades.
– Mast
Commented Jul 26, 2020 at 10:16
• Some people use electric drills as coil winding machines, and hold the wire spool by hand. Commented Jul 27, 2020 at 9:35

The magnetic field in the region between the arms would be relatively uniform in direction, but non-uniform in intensity. Below, I've attached an image of the field that I made using very simple simulation software (note: this is extremely simple software meant for didactic use only. its results are not necessarily representative of reality); notice how the magnetic field is more intense (whiter) on the left side, near the permanent magnet, and less intense (greener) as you move to the right.

If I adjust the intensity a bit to better show it, you can also see that the field between the arms is far lower in magnitude than the field nearer the permanent magnet:

This may be good enough for you. Or it may not. Personally, I'd use a Helmholtz coil and just deal with having to wind the thing manually; it's tedious, but at least you only have to do it once.

• Wow, yes this is sufficient. I didn't know falstad had such a simulator. I will experiment with it a bit more. Thank you very much! Commented Jul 25, 2020 at 18:51

Looking at the following three bits:

I want to see if a design using permanent block magnets is feasible in terms of cost and construction. The volume inside the chamber is approximately 13cm x 13cm x 13cm.

To reduce construction costs, I am planning to laser-cut many pieces and stack them

This is an experimental prototype design, in which I care more about the field homogeneity rather than the field strength itself.

and this answer then it seems you can have some fun adjusting the shapes of your pole edges to try to get more uniformity of field strength and, if you need it, of field direction.

There is another approach that you should consider, it's usually the solution people adopt when they need to produce a volume of uniform magnetic field. You could build a Helmholtz coil.

In the first image the field is in the vertical direction and the upper and lower coils have current in the same direction.

Sources: 1, 2, 3

You can get a uniformity of about 1% over a significant volume this way, and with a single knob you can adjust the strength

If you need to cancel the Earth's field, or if you want to be able to point the field in any direction you can build three sets of interlocking Helmoltz coils and with three knobs you can point the field any way you like.

Here is a higher order three-axis set of coils that uses a second set in each axis to improve the uniformity even further and over a larger volume. It is discussed in the Physics SE question How are these “supplementary” or “satellite” Helmholtz coils used?:

Annotated screen shot from the NASA video MAVEN Magnetometer

Here is a wooden form on which you can see three pairs of interlocking grooves for a three-axis configuration for applying varying but uniform field strengths and directions to the magnetometer on the deep space probe Mariner 3. It is discussed in the Space SE question Why is there a large wooden ball on Mariner 3's magnetometer?.

Source: Photograph Number 293-6619Ac. Image credit: NASA/JPL-Caltech.

You'll get a field. It will produce a fairly uniform field, for some values of 'fairly' that you may not recognise. There are FEMM solvers, some free, that will show you how horribly non-uniform a field you'll get. It all depends on your specification, does uniform mean +/- 10%, or +/- <1ppm (as required in MRI)?

You have a strong axis of asymmetry, with strong magnets and a lump of iron off to one side. This will put an overall slope on your field.

You have flat faces, so the field will be uniform over a tiny volume dead-centre, and fall off towards the edges. You'll be able to counter this effect by reducing the distance between the faces as the distance from the centre increases, your laser cutting flexibility could come in handy. In a hybrid solution, you could use permanent magnets to produce the bulk of the field, then tune for uniformity using 'shim coils' (as they're called in MRI imaging) to tweak up the field shape.

With modern high field magnets, you may be better off abandoning the return field limb, and simply using two arrays of small strong magnets held onto two separate, facing, flat iron sheets by their own attraction. The field could then be tuned to uniformity by adjusting the density of the magnets, or by adding iron to the ends to change the spacing.

• This is really excellent advice! At some distance a mu-metal enclosure might be helpful to keep stray fields from extending into the work area, possibly causing trouble and attracting random bits from being pulled in and getting stuck.
– uhoh
Commented Jul 27, 2020 at 4:12
• Mumetal is good for some sorts of sheilding. For shielding your work area, think about the concepts of a Halbach array Commented Jul 27, 2020 at 5:22
• Okay I thought about it. I guess you're suggesting adding even more magnets, farther out, so that in the far field the thing looks like a higher order multipole rather than a dipole, and thus the field drops far more quickly at large distances. Compared to rummaging around old storage rooms and basements for some ugly used mu-metal, this sounds far more fun and cool-looking, but sooner or later someone's going to pull out their car keys and see what happens. But until that time, it will seem like genius! :-)
– uhoh
Commented Jul 27, 2020 at 5:34
• If you only want to protect people's car keys, there's no need for mu metal, ordinary iron / cheap mild steel will do. I don't know whether you want an open volume to work within, or whether a closed box would be feasible, albeit with a door. The ideal configuration, both from uniformity of field internally and lack of field externally would be a hollow iron or steel cylinder, perhaps 2 to 4 times the diameter of your work volume. Place the magnets on the inside of the circular end faces. Ah! What do you mean by 'work area'? Commented Jul 27, 2020 at 7:38
• mu-metal would be lighter and you can simply cut it and bend it into shape. I have no idea what I mean by 'work area' exactly, just areas that are uncontrolled and people may be doing things that are affected by magnetic fields or with objects that could end up stuck to the magnets. Uncontrolled and/or unexpected stuff.
– uhoh
Commented Jul 27, 2020 at 9:03

Even the Helmholz coil standard for uniform magnetic field fails at points other than the exact center. How uniform must it be? Uniformity will be perturbed by magnetic substances like water or liquid oxygen. The bottom line: You can’t get a uniform magnetic field over a non-zero volume, just like you can’t get absolute zero temperature.