Modeling a Permanent Magnetic as a Dipole?

[dedicateddan]

I am trying to approximate the field of a permanent neodymium magnet as that of a magnet dipole. The magnet in link the below can be modeled by a magnetic dipole of what strength?

http://www.magnet4less.com/product_info.php?cPath=11&products_id=123

Thanks in advance!

 

[marcusl]

A dipole is not a very useful model of a magnet unless you are trying to calculate the fields very far away. For close-in effects you might try placing effective (virtual) magnetic charges on each face. There is no good way to calculate this from the information available on the web page, the best you can do is a very rough guesstimate. Have you taken a vector calculus based electricity and magnetism class?

 

[dipole]

I think you can make the approximation that the magnetization is constant over the volume of the magnet, and so is the B-field and H-field.

You can then use this as a boundary condition, and the standard boundary conditions for the B and H fields at the surface of the magnet and infinity to solve for the magnetic potential (hopefully!).

I don't know how marcusl's method would work because I don't know how you'd know how to distribute the magnetic charges, maybe he can explain.

 

[dedicateddan]

@marcusl, yes, I have taken E&M and vector calculus.

I'm running a simulation for a researcher who has actually built a device which involves passing neodymium magnets through coils to produce electricity.

It seems silly, but I'm really just trying to figure out the magnetic field produced by a permanent magnet. I modeled the permanent magnet as a magnetic dipole because I had dealt with those in courses before and they seem to produce qualitatively reasonable results. I'm really wondering how to turn specifications, like those found below, into a description of the B-field produced by the magnet. Any insight or references describing the B-fields of permanent magnets would also be appreciated.http://www.kjmagnetics.com/proddetail.asp?prod=DY0X0

 

[marcusl]

I think you can make the approximation that the magnetization is constant over the volume of the magnet, and so is the B-field and H-field.

Actually B is nonuniform inside due to the "demagnetizing field", which is nonuniform for a cylinder. This is one reason that magnets are non-trivial to model.

It's been years (decades) since I looked at this, so I'll try to reacquaint myself with the methods tomorrow and write back on the weekend.

 

[marcusl]

Here are some thoughts. Simple models of a cylindrical magnet are 1) a uniform volume magnetization, w) an equivalent surface current K that replaces the volume with an effective solenoid or 3) as equivalent magnetic charges on the pole faces. All of these are strictly incorrect--but they still can be used to estimate the field everywhere outside of the magnet. (A dipole model, on the other hand, is useful only at distances that are large compared with the magnet dimensions.) The reason it may not pay to construct a high fidelity model, which includes non-uniform magnetization resulting from the demagnetizing field, is because of the large uncertainties you have about the actual magnet. For instance, your link lists a field strength but no detail about how it was obtained. Is that the highest saturated value of B inside the material? An average value? Was it measured outside? Where? (If a Hall effect probe was used, it likely represents some sort of average across the pole face at a distance of some mm--which is not small compared to the magnet dimensions).

In short I'm agreeing with "dipole" above; a high fidelity model is not justified by your low fidelity data, so you might as well use a lower fidelity model. You will get guesstimates with rather large error bars but this may still be useful to you.

 

[dedicateddan]

That is some very useful input, marcusl. I will try some of the models that you suggested and compare the results to the ones that I have for the dipole. I will try to post an update after I've done this.

 

[dipole]

Here are some thoughts. Simple models of a cylindrical magnet are 1) a uniform volume magnetization, w) an equivalent surface current K that replaces the volume with an effective solenoid or 3) as equivalent magnetic charges on the pole faces. All of these are strictly incorrect--but they still can be used to estimate the field everywhere outside of the magnet. (A dipole model, on the other hand, is useful only at distances that are large compared with the magnet dimensions.) The reason it may not pay to construct a high fidelity model, which includes non-uniform magnetization resulting from the demagnetizing field, is because of the large uncertainties you have about the actual magnet. For instance, your link lists a field strength but no detail about how it was obtained. Is that the highest saturated value of B inside the material? An average value? Was it measured outside? Where? (If a Hall effect probe was used, it likely represents some sort of average across the pole face at a distance of some mm--which is not small compared to the magnet dimensions).

In short I'm agreeing with "dipole" above; a high fidelity model is not justified by your low fidelity data, so you might as well use a lower fidelity model. You will get guesstimates with rather large error bars but this may still be useful to you.

Interesting, I'm taking an EM course but we never got into the demagnetizing field - I'll have to read about that.

And I can see now that the choice of name "dipole" was a poor one for threads like this. :)

 

[marcusl]

And I can see now that the choice of name "dipole" was a poor one for threads like this. :)

Or a brilliant one...