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On May 5, 2021, at 2:38 PM, John Denker via Phys-l <firstname.lastname@example.org> wrote:
On 5/5/21 10:52 AM, Carl Mungan wrote:
[a] now I'm back to my original question: Given that the Amperian
currents are microscopic, I would think they wouldn't be reduced by
We agree they are not reduced by lamination.
They depend only on the relative permeability, which is big for
Well, they depend on that, but not only on that.
[b] So why doesn't the self-inductance of a Pasco coil increase by
thousands (instead of only 10) when I put a laminated iron bar into
its core? The magnetization field should only depend on the Amperian
currents, not on the actual continuity of the field line loops,
shouldn't it? A whole bunch of adjacent microscopic loops act like
one big loop, right?
It seems to me [a] and [b] are completely different questions. That
is, lamination is one thing, while un-closed magnetic circuits are
something else entirely. The two issues are orthogonal, geometrically
as well as metaphorically.
Let's focus on a DC magnetic field, in which case the laminations
don't matter at all, and the eddy current issue doesn't arise at
all, which is helpful. So [a] is now moot and we focus on [b].
Magnetic field lines are endless. This is one of the Maxwell equations.
Suppose, very hypothetically, that the applied field causes all the
electrons in the iron to align in the desired ferromagnetic way.
Question: What happens to all those field lines when they come to
the end of the iron bar?
Answer: The lines must spill out into empty space. Hypothetically,
the field is 10,000× stronger than it would have been without the
bar. The energy density in the air is higher by a factor of
100,000,000 ... which is exceedingly unfavorable.
Non-hypothetically, the lines will re-arrange themselves to make
this not happen.
In contrast, if you arrange a /closed/ magnetic circuit so the
field lines have an endless path /within/ the iron, there will
be no regions with high energy density.
I'm guessing here, but perhaps today's misconception arises from
putting too much weight on the precept that "all physics is local".
That precept is true as stated, but it needs to be applied carefully.
It needs to be applied to the /fields/ not just the particles. The
field of a point charge is not confined to the immediate vicinity
of the particle. The field near the particle has to be /consistent/
with the field next door, which is in turn consistent with what's
next door to it, and so on to the end of the universe, in accordance
with the field equation at every point (not just at the location of
Specifically, in this case, you can't just look at what's happening
to one ferromagnetic electron in the middle of the iron. You have
to look at the big picture.
Undergrad students (and some bright HS students) can solve Laplace's
equation for the static electric field using iterative relaxation
methods to achieve the desired /consistency/. Closely analogous
methods can be used to solve for the static magnetic field, including
iron pole pieces, with or without gaps. The relaxation process gives
you a way to appreciate how local physics can enforce global requirements.
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