# Is This Correct Description of Magnetic Saturation?

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• audioresearch
audioresearch
I believe that if a put current through a coil of wire and if I have unlimited power to force through that current and if the coil can accept unlimited power without being degraded, I could produce a magnetic field in a vacuum of unlimited strength-is that correct? But supposedly if I applied such a magnetic field to a permeable material, there will come a point where applying stronger and stronger magnetic fields from the coil will no longer increase the magnitude of the magnetic field inside that material and that is called saturation. Therefore, if I understand this correctly (do I?), the presence of a permeable material somehow limits the maximum magnitude of a magnetic field that can exist inside it due to saturation-is that true? If it is true, please explain to me how the presence of a permeable material can possibly reduce magnetic field strength from what it would have been in a vacuum? What mechanism does that? Would it be true that if I want to have the strongest possible magnetic field, I should avoid using a permeable material since using such material limits the maximum magnetic field strength?

audioresearch said:
I believe that if a put current through a coil of wire and if I have unlimited power to force through that current and if the coil can accept unlimited power without being degraded, I could produce a magnetic field in a vacuum of unlimited strength-is that correct?
Yes, this is true in principle.
audioresearch said:
Therefore, if I understand this correctly (do I?), the presence of a permeable material somehow limits the maximum magnitude of a magnetic field that can exist inside it due to saturation-is that true?
No, that's not true. From https://en.wikipedia.org/wiki/Saturation_(magnetic):
The relation between the magnetizing field H and the magnetic field B can also be expressed as the magnetic permeability: 𝜇=𝐵/𝐻 or the relative permeability 𝜇𝑟=𝜇/𝜇0, where 𝜇0 is the vacuum permeability. The permeability of ferromagnetic materials is not constant, but depends on H. In saturable materials the relative permeability increases with H to a maximum, then as it approaches saturation inverts and decreases toward one.
Due to saturation, the magnetic permeability μf of a ferromagnetic substance reaches a maximum and then declines:

Since the relative permeability of vacuum is one, this means that for large enough fields ##H##, the ferromagnetic material behaves magnetically more and more like vacuum. So ##H## can in principle be increased without bound even inside of a saturable material.

SammyS
Got it, thanks very much. Usually, for me, Wikipedia is not too easy to follow on involved scientific matters which is why I did not look there for an answer, but in this case it was easy to understand. I think my understanding got thrown off because some explanatory information I read incorrectly stated no further increase in B with H happened once saturation was reached.

It's clear in Gaussian units. ##{\bf B=H}+4\pi{\bf M}##. ##\bf M## reaches a maximum, so
##\bf dB=dH.##

audioresearch said:
because some explanatory information I read incorrectly stated no further increase in B with H happened once saturation was reached.
This isn't an uncommon thing to read. The problem is that the permeability of most magnetic core materials is so high that μo is considered insignificant in many situations. If I have μr=3000 initially, I might treat a switch to μr=1 as nothing.

mu is meaningless in ferromagnetism. Beyond saturation, if you say ,mu=B/H, then mu is still huge, NOT near 1.

Meir Achuz said:
mu is meaningless in ferromagnetism. Beyond saturation, if you say ,mu=B/H, then mu is still huge, NOT near 1.
OK, but that's not what we would say for a non-linear system. What about ##\mu = \frac{\partial B}{\partial H}##?

Please give a source for ##\mu=\frac{\partial{\bf B}}{\partial{\bf H}}##.
If there are two different definitions, that makes ##\mu## even more meaningless for ferromagnetism.
My post #4 explains it. Why introduce ##\mu##?

Meir Achuz said:
Please give a source for ##\mu=\frac{\partial{\bf B}}{\partial{\bf H}}##.
If there are two different definitions, that makes ##\mu## even more meaningless for ferromagnetism.
My post #4 explains it. Why introduce ##\mu##?
It turns out to be a useful thing for engineers to talk about with each other, that's why it's all over the internet. You don't have to use it.

I have designed what will be one of the worlds largest conventional magnets once completed. I have been paid real money to do this. That may not make me an expert, but it makes me a professional at leas.

μ as a function of B (or equivalently H) is an extremely useful way of thinking about magnet behavior. Even, perhaps especially, ferromagnets. Is the relationship between B and H proportional? Or is it additive? That depends on where you are on the B-H curve, and to some degree, hysteresis.

If you want to know what the field is doing, you really need to look at energetics. The first field line costs much less to go in the steel than the nearby air. The last field line, if you are saturated, costs the same.

DaveE
As a PS, "my" magnet is, by design, partially saturated. The field in one region is set by the saturation properties in another. This is done to make the field in the non-saturated region more stable and uniform, and to do it with fewer ampere-turns.

Meir Achuz said:
Please give a source for μ=∂B∂H.
1) All of the internet. Wikipedia, for example.
2) All of the magnetic core manufacturers. Mag-Inc, for example.
3) Applications of Magnetism, J. K. Watson. My old undergrad textbook. Sorry, it is an engineering book, so you can ignore it.

weirdoguy
As a PS, "my" magnet is, by design, partially saturated.
In power supply circuits this is also the normal case. Size, weight, cost, etc. say don't have "unused" core material. Core loss (efficiency) is the tradeoff.

edit: Except we want "equally partially saturated" (spatially) for efficiency. Fortunately the core geometries are designed for this, so circuit designers don't have to do the FEA stuff. Even if we do something like a "half turn" on an E core, it's still just a slightly more complicated lumped element. No real core design involved. So, different than what you described.

It's also not uncommon in some structures to have small metal bits (brackets, etc.) that saturate early and aren't really part of the intended core. This is why initial permeability can be misleading. You want to excite it up towards the operating point to see what's left that actually matters.

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The parts costs alone for "my" magnet comes out to several million dollars. So it is worth having an engineer doing FEA. By seeing where the field goes, we can redistribute the steel to save money and/or improve performance. The steel cost is about 4x the copper cost.

I would have loved to use "electrical steel", but the cost was prohibitive. The problem with that is that the literature is rather spares on magnetic properties of most non-electrical steels. A36 is an exception. We're using 1006, which was used in two other experiments, so we have somewhat better B-H knowledge than for most steels.

Most physics texts treat μ as a constant. So I understand where people get this idea. But real magnets are not frictionless planes or stretchless ropes.

DaveE
Most physics texts treat μ as a constant. So I understand where people get this idea.
Plus most circuit designers either buy a component or design a custom one using standard cores and materials. They are typically not nearly optimized magnetically like big or complex systems. With lots of design margin and parts designed to be used by posers (like me), you are allowed to make some simplifying assumptions.

I think it's fine to just teach the 1st order version. Because if you go deeper it's all Maxwell's Equations and materials science where everything is a special case.

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