Re: magnetism question
- From: "PD" <TheDraperFamily@xxxxxxxxx>
- Date: 13 Dec 2005 07:42:39 -0800
muknot@xxxxxxxxx wrote:
> Hi I have a question:
>
> Say you have a flux distribution due to a magnet, then you place a
> piece of iron beside the magnet and you get a new flux distribution.
> The flux density in the iron will be greater than the flux density in
> the surrounding air. Why is this? Is it because the magnetization of
> the iron creates additional flux in it, thus leading to more flux
> density, or is it because the flux from the magnet prefers to travel
> through the iron (rather than the surrounding air), thus leading to a
> greater flux density or do both these effects contribute to a greater
> flux density in the iron? Also if the flux from the magnet prefers to
> travel through the iron, what's the reason for this (just saying that
> it has higher magnetic permeability isn't much of an explanation)?
>
> Another question I have is if you place a piece of iron in a magnetic
> field that saturates it, and then remove a bit of iron (create a pit),
> from the surface of your sample, the flux will "leake" out of your
> sample. I don't understand why this happens, why doesn't the flux just
> continue to travel through the air (where the pit is) with the same
> distrubiton it had in the iron -- why does it have to take up a
> greater volume in the air?
>
> Thanks.
Interestingly, I once made a fairly dramatic mistake along these lines.
The mission was to instrument a large, iron-core toroidal magnet by
inserting a Hall probe into a slot penetrating the iron.
I attempted to account for the field by superimposing the field of a
slotless toroid (which I could model with a mesh relaxation program
that solved the differential equation), plus the *negative* of a
magnetized piece of iron that would fit in the slot. The idea was to
map how far the slot affected the field elsewhere in the metal. The
field of the "slot piece" was estimated with a magnetic circuit
argument, the slot creating a certain "resistance" to the field were
the permeability is that of air.
Though plausible, the superimposition only works on linearly adding
fields, and ferromagnetism is an inherently nonlinear problem, because
the permeability is a steeply falling function near saturation. This
mistake resulted in Hall probe values that were consistently 20% lower
than the (fortunately) redundant loop-induction coils provided.
==============
But to answer the OPs question, the reason *why* the field favors the
iron and not the air is an energy minimization. The energy stored in
the magnetic field is essentially a volume integration of the entire B
field over all space, where the total flux is constrained by Ampere's
law and where the continuity of the field at material boundaries is
given by boundary conditions imposed by Maxwell's equations. All that
mumbo jumbo aside, it's energetically favorable to pack as much of the
field into a small volume, and it can do that where the permeability is
high so that you get a lot of field for the same current. It can't
*all* reside inside the metal because of the boundary conditions.
PD
.
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- From: muknot
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