How do magnetic "return paths" really work?

• I
While reading about how magnetic flux works, I've come across two concepts that seem to contradict each other:

Concept A: http://www.emfs.info/what/adding/ adding magnetic fields is simply vector addition. In other words, magnetic fields are always acting independently, and the sum of flux at any given location in space the just the sum total of independently behaving magnetic fields at that point in space.

Concept B: putting magnets or permeable materials close together alters the "return path" of their magnetic flux lines. For example, a "closed core" transformer versus a "shell core", where the idea behind the shell is to bring the magnetic return path of the coil closer to the coil. This would suggest that the magnet flux of any given atom is not a fixed shape, but that it's shape can altered by other magnetic fields, which contradicts the idea that a combination of magnetic fields is simple vector addition.

Are magnetic lines of flux really "shaped" by the other magnetic things around them, or do they always maintain a particular shape no matter what, and the concept of guiding "returns paths" merely an abstraction?

berkeman
Mentor
While reading about how magnetic flux works, I've come across two concepts that seem to contradict each other:

Concept A: http://www.emfs.info/what/adding/ adding magnetic fields is simply vector addition. In other words, magnetic fields are always acting independently, and the sum of flux at any given location in space the just the sum total of independently behaving magnetic fields at that point in space.

Concept B: putting magnets or permeable materials close together alters the "return path" of their magnetic flux lines. For example, a "closed core" transformer versus a "shell core", where the idea behind the shell is to bring the magnetic return path of the coil closer to the coil. This would suggest that the magnet flux of any given atom is not a fixed shape, but that it's shape can altered by other magnetic fields, which contradicts the idea that a combination of magnetic fields is simple vector addition.

Are magnetic lines of flux really "shaped" by the other magnetic things around them, or do they always maintain a particular shape no matter what, and the concept of guiding "returns paths" merely an abstraction?
Magnetic fields are attracted to ferrous metals, and magnets are generally made from ferrous metals. So when you bring the two magnets near each other, that will cause a distortion in their fields because the magnets are made from ferrous metals. It's not the fields interacting with each other, it's the fields being distorted by the material nearby.

Magnetic fields are attracted to ferrous metals, and magnets are generally made from ferrous metals. So when you bring the two magnets near each other, that will cause a distortion in their fields because the magnets are made from ferrous metals. It's not the fields interacting with each other, it's the fields being distorted by the material nearby.

How can combining magnetic fields be simple vector addition if their fields are distorted? You'd no longer have "field A + field B", but "somehow distorted field A + somehow distorted field B". Does that make sense?

berkeman
Mentor
Here is an image of the B-field lines of a flat field being attracted to a ferrous sphere -- the simulation shows the shielding effect excluding the field from the inner hollow part of the sphere.

http://www.magneticshields.co.uk/images/magnetic-field-flow.jpg

berkeman
Mentor
How can combining magnetic fields be simple vector addition if their fields are distorted? You'd no longer have "field A + field B", but "somehow distorted field A + somehow distorted field B". Does that make sense?
You can combine them if the source is not a ferrous metal. For example, you can combine the B-fields generated by two current-carrying wires with simple vector addition. (As long as the wires are copper or some other non-ferrous metal).

You can combine them if the source is not a ferrous metal. For example, you can combine the B-fields generated by two current-carrying wires with simple vector addition. (As long as the wires are copper or some other non-ferrous metal).

Do you have a source for this? The source I linked above did not mention caveats about magnetic flux lines only vector summing in non ferrous mediums.

I've read that overlapping magnetic field obey the super position principle:
https://en.wikipedia.org/wiki/Superposition_principle
In physics and systems theory, the superposition principle,[1] also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. So that if inputA produces response X and input B produces response Y then input (A + B) produces response (X + Y).

Furthermore, when a ferrous material is exposed to a magnetic field, it becomes a magnet also, so AFAIK, at that point you're rally just talking about yet another magnet being added to the equation, vector summing in the same manner as the permanent magnet that caused the ferrous material to magnetize.

berkeman
Mentor
Do you have a source for this?
BTW, I should mention that I was referring to static B-fields. If they are AC fields, they can induce currents in the other nearby conductors, which will change the overall combined B-fields.
when a ferrous material is exposed to a magnetic field, it becomes a magnet also,
Not necessarily. It depends on the material. The wider the hysteresis curve for the material, the more residual magnetization you will have. But some materials have pretty skinny hysteresis curves...

http://www.intechopen.com/source/html/48734/media/image28.jpeg

AFAIK, the hysteresis curve is caused by the (un)willingness of the magnetic domains in the ferrous material to align, and/or re-align later, as is dictated by the particulars of the physical structure at the atomic level, but once they align, it is essentially a proper magnet from that point onward.

If it's true that the concept of a guided magnet return path is an abstract concept, this would be big news to me, as I've never seen it stated as such.