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Re: [Phys-L] magnetic circuits ... was: change in inductance with iron core

On 5/5/21 4:00 AM, Carl Mungan wrote:

1. As I understand it, the reason we laminate the cores in the first
place is to reduce eddy current loops which cause energy

But now it appears there’s a trade-off in that doing so also causes
a big drop in the inductance gain.
No drop. No trade-off; see below (*).

Is it sort of the case that eddy currents create magnetic fields
which helps increase the inductance,
Nope. Just the opposite. I might know where this misconception
is coming from, as discussed below (**), but for now let me simply
remark that eddy currents make it /harder/ for field lines to
enter the material. The poster child for this is a superconductor,
which is nearly 100% /diamagnetic/, which is the opposite of what
you want for an ideal transformer or inductor.

at the same time those currents lead to Joule heating?

Yes, eddy currents produce heating. They are 100% bad if you want
an ideal transformer or inductor.

So what I would ideally want is a ferromagnetic material that has
super high conductivity, so I get lots of eddy currents but little
resistive dissipation?

Nope. Eddy currents are not what you want. See below (**).

On 5/5/21 6:00 AM, Sam Sampere via Phys-l wrote:

The laminations are parallel to the field, so you made a parallel
circuit magnetic field. I think not much decrease. Each laminate
sheets completes the magnetic circuit. Take and old transformer and
go band saw it in half (yes, that is both a noun and a verb). You'll
easily see the sheets forming complete loops in the direction of B.

That's all true.

(*) In my own words:
1) Things are aligned so that the magnetic field lines lie mostly
in the plane of the lamina. You can confirm this by looking in
your front closet (or visiting the hardware store). Look at the
orientation of the lamina in the core on a doorbell transformer.
2) Eddy currents want to flow in big loops perpendicular to the
field lines, so they are trying to cross from one lamina to the
next, but they can't, because the lamina are electrically insulated.
3) It's even better than that, because the insulation has virtually
infinite electrical resistivity, whereas its magnetic reluctivity
is not infinite; it cannot be bigger than unity, which is bigger
than iron by a factor of 10,000, but not infinite. So a very thin
insulating layer is a win/win. (You can check that they do in fact
use a very thin layer of insulating varnish, not a thick layer of
plastic or rubber.)


(**) At the next level of detail, i.e. the next level of physical
modeling, visualization, and insight:

a) Consider a simple electromagnetic, in the shape of a solenoid.
For present purposes, that includes a simple coil, which is just
a very short solenoid. It produces a magnetic field in the middle.

b) Similarly, a permanent bar magnet has a magnetic field.

c) A bar of magnetically-soft iron inside a solenoid also produces
a magnetic field, which is a multiple of the field the solenoid
would have produced by itself.

d) We can unify item (a) with items (b) and/or (c) by imagining
that there are little loops of current (Amperian currents) within
the iron. For the soft iron (c) the Amperian currents are more or
less proportional to the applied field at any given time.

e) There are also eddy currents. These are proportional to the
rate-of-change of the applied field. That is to say, voltage
equals flux dot. That's one of the Maxwell equations.

f) Here's where things get interesting: The Amperian currents
have the same orientation as the eddy currents. They circulate
/around/ the magnetic field lines. However (!) they are not the
-- For starters, one depends on the value of the field, while
the other depends on the rate-of-change of the field.
-- For a positive and increasing field, the two contributions
are in opposite directions. The Amperian currents magnify
the field, while the eddy currents oppose the change in field.
-- See the following item (g).

g) Laminations affect the two contributions very differently.
Specifically, the Amperian currents are imaginary. They are
not currents in the classical sense. Ordinary paramagnetism
and ferromagnetism depend on the /spin/ of electrons, which is
definitely non-classical, as Goudsmit and Uhlenbeck emphasized
on Day One. So there is no temptation for Amperian "currents"
to cross from one lamina to the next. To repeat: the Amperian
"currents" flow in infinitesimal-sized loops, while the eddy
currents flow in huge loops. So if you want an ideal inductor
or transformer, once again lamina are a win/win. You can oppose
eddy currents and cultivate paramagnetism at the same time,
even though both "currents" have the same orientation, i.e.
flowing /around/ the magnetic field lines.