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I am new to learning magnetic fields and Magnetic permeability caught my attention. From what I understand higher the permeability of a material, the less it opposes the magnetic fields it is placed in.

However, my confusion is, when ferromagnetic materials, such as soft iron, which also have a very high permeability, are placed in a magnetic field it induces a magnetic field oppose to the first magnetic field which it was placed on (from what I understand, that's how materials like iron, which doesn't show magnetic properties when they are alone, but get attracted to magnets when placed near them, because one side of the material forms an opposite pole to the magnetic pole near it, thus attracting to it but also forming a magnetic field opposing to the magnets magnetic field)

So why I am confused is, how does materials like soft iron, as I reasoned earlier, show higher permeability, if they oppose the magnetic field they are in? Feel free to correct me, because I feel like I have misunderstood something. Thank you in advance.

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  • $\begingroup$ if you take a coil with a ferromagnetic core in a shape of a ring the $H$ field is essentially the same inside with the core as without it but not so for the $B$ that is increased in proportion to the material permeability. This is why engineers like the $H$ field because with the current they can control it in this setup. Now cut a very narrow gap in the core and all of the sudden the whole world changes , inside the core the B/H fields drop but in the gap both get concentrated, the narrower the gap the stronger the concentration. The poles develop charges opposing the original field. $\endgroup$
    – hyportnex
    Commented Aug 20 at 15:17

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Magnetic permeability is confusing**. When dealing with permeability, there are actually THREE related field quantities: The B-field, the H-field, and the M-field. It's difficult to define these all in a way that is both intuitive and technically correct, so I won't try except to say that external fields are generally thought of as H whereas internal fields are generally thought of as B (although there is an internal H field as well). People argue about which one, B or H, is more "fundamental" but I leave those discussions to the philosophers. It's like stress and strain -- different but intertwined. Either way, the B vs H or B vs M curve of a material determines the magnetic permeability of the material. When a "soft" magnetic material (meaning highly permeable but NOT permanently magnetized, approximated by constant permeability $\mu$) is placed in an external field, the internal H-field tends to approach zero (depending also on geometry and value of $\mu$) and is more or less replaced by the M field, representing the magnetization effects on the material. The B field can be thought of as the total of both these fields. Integrating the value of M over the volume of the material gives you the effective magnetic moment $m$. But when you take away the external field, $M$ and $m$ go to zero (as do B and H).

For a situation where the H field of the material "opposes" the B field, you have to consider "hard" magnetic materials with permanent magnetization. In that case, the B vs H curve is more like a loop - not linear at all, and $\mu$ varies depending on the point of interest. There does not need to be an external H field to magnetize the material because it is already magnetized (although an external H was needed to achieve that). To describe the state of magnetization, the relevant point on the B-H curve is in the second quadrant with positive B and negative H, where the H can be thought of as "internal." The magnetization M is positive as before.

** To add to the confusion, there are at least three different unit systems in use, so you may see equations like $B = H$ instead of $B = \mu H$ or factors of $4 \pi$ floating around in some equations but not others. This makes the subject especially hard to self-teach, in my opinion.

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  • $\begingroup$ Its not hard to understand what B,H and M are.The electrical analog is E,D and P. $\endgroup$
    – Root Groves
    Commented Aug 20 at 14:18
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    $\begingroup$ Well, it depends on which field you consider. The B field is continuous inside (and outside) the permanent magnet, but the H field is not; this is the field that reverses. See en.wikipedia.org/wiki/Demagnetizing_field $\endgroup$
    – Mariano G
    Commented Aug 21 at 12:53
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    $\begingroup$ @donthababakka A permanent magnet has practically zero magnetic permeability. It is already magnetized. quora.com/What-is-the-permeability-of-a-permanent-magnet $\endgroup$
    – Markoul11
    Commented Aug 21 at 12:56
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    $\begingroup$ That's true for commercial permanent magnets because an "efficient" magnetization process will align almost all of the internal magnetic domains. So there isn't much material left to magnetize that isn't already. But it's not true for every magnetized object. $\endgroup$
    – Mariano G
    Commented Aug 21 at 13:09
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    $\begingroup$ This graphic may be helpful. armsmag.com/news-B-H-curve-neodymium-magnets.html $\endgroup$
    – Mariano G
    Commented Aug 21 at 13:10

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