My nephew is studying the properties of magnetism and asked me to to explain how to calculate magnetic force. I started to google for an in depth explanation and maybe a more simplistic answer. These two articles caught my eye but have left me wondering if either are correct judging by the replies to the second one.
http://www.physics.princeton.edu/~mcdonald/examples/magnetic_force.pdf

https://www.physicsforums.com/insights/permanent-magnets-ferromagnetism-magnetic-surface-currents/

Maybe my brain is seizing up, I used to be able to analyse this stuff when I was in my 20's-30's, but in my 70's now it's not so easy!

 

My nephew is studying the properties of magnetism and asked me to to explain how to calculate magnetic force. I started to google for an in depth explanation and maybe a more simplistic answer. These two articles caught my eye but have left me wondering if either are correct judging by the replies to the second one.
http://www.physics.princeton.edu/~mcdonald/examples/magnetic_force.pdf https://www.physicsforums.com/insights/permanent-magnets-ferromagnetism-magnetic-surface-currents/

Maybe my brain is seizing up, I used to be able to analyse this stuff when I was in my 20's-30's, but in my 70's now it's not so easy!

The comments by ZapperZ at PF are correct.

And this, to me, is the SOURCE of the confusion, and the reason why I objected to the article. Not only did it not explain everything about ferromagnetism, I also claim that it explains nothing about ferromagnetism. It describes the FIELD generated by a ferromagnet, but it says nothing about ferromagnetism. Ferromagnetism is the material, the formation of magnetic ordering within the material. The result of such ordering is the magnetic field. The title of the article is severely misleading when you claim "Permanent Magnets Explained by Magnetic Surface Currents". This was my objection from the very beginning – the use of that language! Claiming that "permanent magnets explained by magnetic surface currents" means that the origin of this permanent magnet is this surface currents. Even you have admitted that this isn't true, but yet, the misleading title, and the first sentence in the article made it sound as if this IS the "explanation" for a ferromagnet. It isn't. It is a way to "explain" the FIELD generated by the ferromagnet. It doesn't explain how ferromagnetism happens. You may think this is a trivial and subtle point, but it isn't, as can already be seen by the misunderstanding made by previous "lay-man" post. If this was an internal note among physicists, I wouldn't have wasted my time because we all know the full story. But this is meant for students and also people who do not have enough understanding of physics to be aware of such things as quantum magnetism. They will walk away thinking that a permanent magnet becomes one due to all these surface currents. That is wagging the dog! Zz.

I am talking about Maxwell's equations formulated in terms of magnetization or in terms of bound currents. Maxwell's equations do not explain magnetization either way, it is phenomenological either way. I don't know why this is rather difficult to understand. Maybe I'll try it this way: Quantum magnetism explains why such-and-such a material is a ferromagnet. Once it has become a ferromagnet, it then produces a magnetic field. This magnetic field can then be modeled as being produced by some "surface currents". Do we have a problem with the statements I made above? If yes, what is the problem? If no, then surface currents cannot explain the existence of a permanent magnet/ferromagnet. It can describe the FIELD generated by the magnet, but not how it became a ferromagnet. If the title of this Insight article reads "Magnetic Fields of Permanent Magnets Described by Magnetic Surface Currents", I would have zero issues with it. Zz.

Reference https://www.physicsforums.com/insig...tic-surface-currents/comment-page-3/#comments