Photo of electromagnet with arrow showing approximate path of measurements

I work in an experimental research lab. I made an electromagnet by having the machine shop cut through a toroid core and hand-winding wire around it. The objective is to have a region of uniform magnetic field above the gap for testing my devices. (The cuts on top of the magnet allow for placing a sample holder on top.) The faces of the magnet in the cut are parallel to each other--at least, by the naked eye. I used a Gaussmeter (425 Lakeshore) to measure the strength of magnetic field as a function of position, slightly above the gap, by recording the field strength at every 1mm interval going from one side of the gap to the other.

EDIT: Added arrow in photo to indicate approximate path of where I took measurements. Imagine that this is slightly above the gap.

This is the result I get:

Plot of field vs position

As you see, there's an overall slope, and the part where the field strength starts to rapidly drop off on the right is lower in magnitude than on the left. I need the area in the middle to be uniform across, not sloping.

What is the explanation for why this is happening? It is a single block of the same material, so I would expect the material to be magnetized uniformly everywhere. So each face of the electromagnet should have the same density of magnetic poles, and therefore the field strength should be the same on each side.

Is it that the winding of the wire is uneven on one side compared to the other? That's the only explanation I can think of so far. Maybe if the density of wire windings is greater on the left than on the right, the magnetization would be stronger on the left?

What if I wound it such that only the bottom half of the toroid has wire around it? That would probably reduce the field strength but would it make the magnetization on each face of the cut more equal?

  • 2
    $\begingroup$ Your graph doesn't surprise me. I would have expected that the magnetic field strength wouldn't be perfectly constant between the pole surfaces as a function of height and that there would be a small slope because the geometry of the magnet isn't symmetric as a function of height about the mid-height point of the poles. Look up "Helmholtz coil" for a better magnet design for field uniformity. $\endgroup$
    – user93237
    Apr 21, 2019 at 20:50
  • $\begingroup$ Is the gap really 25 mm wide? And does the horizontal axis of your graph correspond to a horizontal position in your photo? If the field nonuniformity is due to external fields as suggested by @janlalinsky and SamuelWeir, turning thr magnet upside down or at 90 degrees should change the measured field distribution. $\endgroup$
    – S. McGrew
    Apr 22, 2019 at 3:58
  • $\begingroup$ Ok, for extra background (probably should have mentioned in my OP), I have made a previous electromagnet with the exact same design, but both the core and the gap are smaller, and that one DID come out symmetric. Or at least much closer to perfect symmetry than this. It was also tested in the exact same setup and location, so what I want to achieve is doable in principle. I wanted to make a bigger one with a slightly larger gap to have a slightly larger area of uniformity. Larger gap means the core has to be bigger so that the faces of the cut have larger area. $\endgroup$
    – StormRyder
    Apr 23, 2019 at 16:38
  • $\begingroup$ @S.McGrew The gap is actually supposed to be 0.95 inches wide. So it's a bit smaller than 25mm. I didn't start measuring at exactly the edge of the gap because it doesn't matter as long as I capture enough points to show where the uniformity starts to rapidly fall off. Yes, the horizontal axis in the graph corresponds to horizontal position (in mm) going left/right in the photo. That's a good idea of a way to prove whether it's due to external (non-uniform) fields or the magnet--to rotate it and redo the test. I'm pretty sure it's the magnet, though. $\endgroup$
    – StormRyder
    Apr 23, 2019 at 16:55
  • $\begingroup$ Oh and also, of course I know about Helmhotz coils. There are certain reasons why it doesn't really work here. The #1 issue is that it's much harder to produce a strong field due to the lack of a magnetizable core. $\endgroup$
    – StormRyder
    Apr 23, 2019 at 17:05

2 Answers 2


Could it be that your coiling isn’t 100% uniform? More coiling on the left side of the core than the right side of the core may make the field skew?


Your meter measures total field, which is not equal to the field of your electromagnet, but has contributions due to nearby objects and Earth's magnetic field.

Also, the measurement may have been inaccurate, winding is not exactly symmetric, the core's permeability may not be exactly the same everywhere.

To obtain uniform field, one has to take into account these things. In practice several pairs of Helmholtz coils are used to prepare magnetic field of high uniformity - for example, at least one pair to create the desired level of field strength, and another to cancel external bias due to Earth's field.

  • $\begingroup$ "To obtain uniform field, one has to take into account these things." Yes, the point of my question is to take account of all the things that are throwing it off. Right now, the winding is my prime suspect. I'm skeptical that the core's permeability would be so uneven. The difference is close to 10%. Earth's magnetic field should be constant in such a small space, so it would just be an offset. It shouldn't result in a slope. $\endgroup$
    – StormRyder
    Apr 23, 2019 at 16:30
  • $\begingroup$ If the core is perfect, then you are right Earth's field should not contribute to the slope. First I would make sure that this slope is indeed there, try to measure the field with several different methods, and using different fixation methods for the probe and its leads. It may be just some slight asymmetry in the system. For example, in the photo the toroid is close to metallic bodies - try to remove them and see if the slope changes. $\endgroup$ Apr 23, 2019 at 20:21

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