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The ideal transformer is supposed to have infinite magnetic permeability.

Creating infinite magnetic field lines from a finite applied field sounds like... a violation of conservation of energy or something? Is energy conserved?

https://www.duramag.com/techtalk/tech-briefs/magnetic-permeability-why-are-some-materials-attracted-by-a-magnet-and-others-are-not/ Source: What Is Magnetic Permeability?

ocrdu
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artist_and_not_EE_by_training
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    In general, ideal components do not exist but are useful in simplifying some calculations and in understanding basic concepts. Among other things, they do not always obey physical laws that rely on the properties of real components. For example an LC circuit composed of an ideal capacitor in parallel with an ideal inductor would support an oscillating current forever because neither the inductor nor the capacitor would have any losses. Thus an ideal transformer can help visualize certain concepts but you can't use it to demonstrate a violation of something like the conservation of energy. – Barry Feb 02 '23 at 03:12
  • @Barry In addition to what Barry said, ideal components do not exist *because* there is a contradiction somewhere if they did. This contradiction may or may not involve conservation of energy. So if it did violate conservation of energy, so what? It's meaningless. In addition, I think infinite fields already violate conservation of energy so it is meaningless to use them in a scenario and then point out that the scenario violates conservation of energy. – DKNguyen Feb 02 '23 at 05:22
  • Also, note that permeability of real materials changes with flux density (i.e. saturation exists). Therefore, even if you had a material with infinite permeability, it need not stay that way for all flux densities. – DKNguyen Feb 02 '23 at 05:26
  • Materials with zero resistivity exist. But I think an infinite permeability material might lead to infinite energy storage. Not sure. – user57037 Feb 02 '23 at 05:34
  • @mkeith Even in superconductors you can't shove an infinite amount of current through them. If you shove enough, resistance re-appears. – DKNguyen Feb 02 '23 at 05:36
  • The phrasing here makes me suspect "lines of force" playing a harmful role here. That is, that there's been a historical habit of teaching magnetism like it's a mesh of physical wires, which gives an unrealistic impression of conservation laws. To clarify: "lines" are just contours of the fields, they don't actually represent anything physical, and needn't be conserved -- just as contours on a topo map. They will be closed loops, but the number and density isn't significant. So, here, it remains consistent to have infinite/zero amounts. – Tim Williams Feb 02 '23 at 05:40
  • Yes, @DKNguyen that is a limitation. Current density must be kept within limits. – user57037 Feb 02 '23 at 05:43

3 Answers3

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Does infinite magnetic permeability (e.g. for an ideal transformer) violate conservation of energy?

Infinite magnetic permeability produces infinite inductance (even for a single turn coil) and, the rate of change of current that can be produced through an infinite inductance when applying a finite voltage is zero.

Hence, no current can flow in and, no energy can be inputted and, no violation of the conservation of energy.

Creating infinite magnetic field lines from a finite applied field

It can't be done without applying infinite voltage for an infinite amount of time.

Magnetic permeability is a material constant (just like electrical resistivity); it doesn't imply that any source of current is applied that might create a H-field just as electrical resistivity doesn't imply a flow of current due to an applied voltage.

Andy aka
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The piece would "short out" the H field. The energy in a unit volume of a magnetic core is B times H, and -- of necessity -- the H field would be zero. So the energy stored in the core would be zero.

I'm not sure how this would work out with a solenoid core (i.e., an open core). For a toroidal core a simple coil would have infinite inductance (which is expected).

TimWescott
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Infinite magnetic permeability is not an expression of infinite field. It's an expression of zero driving force for a finite field.

As the transformer core material becomes more and more ideal, the same B field needs less and less H field to drive it.

Notice that as the permeability approaches infinity, the energy stored in the material, proportional to B*H, approaches zero as H approaches zero!

Neil_UK
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  • Indeed, even if the energy cost is nonzero, it's perfectly acceptable for fields to self-organize -- ferromagnetism for example. In that case, the energy source is thermal, e.g. a phase change with *anomalous heat capacity*. Such materials largely confine the field to within the material (e.g. individual magnetic domains) with a small bulk/external field, but there's no absolute prohibition against this as well (the heat capacity will just be that much higher). – Tim Williams Feb 02 '23 at 08:56