Re: Driving LEDs with a battery pack

On Sun, 19 Jul 2009 05:14:10 -0700 (PDT), fungus
<openglMYSOCKS@xxxxxxxxxx> wrote:

On Jul 19, 10:09 am, Jon Kirwan <j...@xxxxxxxxxxxxxxxxxxx> wrote:

In effect, __all__ of the energy gets stored in vacuum.

So the iron is just shaping/directing the field?

(And holding the wires in place)

It provides the shorter path, the one taking less energy, so yes.
That's kind of the way I like to look at it. Everything in nature
appears to choose the path of least energy change. A soap bubble
instantly takes up the shape that requires the least energy,
regardless of any nearby structures it also clings to. Things like
that. So the iron just presents a very low energy path for the field,
mostly as I see it because each atom easily aligns if tweaked just a
little by the field and provides a near-zero-energy-hop to help the
field bridge over all that space it otherwise would need to get
through.

The other aspect is that there are an infinite number of 'closed
magnetic bubble surfaces', none of which may cross through each other.
Each 'surface' is 'looking' for the lowest energy circuit through
space, but cannot cross through any other surface. So they 'bunch up'
a lot in the iron, which is the way-easy path, but stack. This is why
we can usually ignore the air around the core, as almost all of the
magnetic bubbles will be found crowded up in the iron core. They
pinch together a whole lot and stay nearby, that way. Eventually,
enough bubble surface density occurs that the 'lowest energy' path
starts to include a little of the space around the iron instead of
entirely within in. But for all intents and purposes, we can imagine
that all of the magnetic field stays in the iron core because that is
far and away the lowest energy pathway for almost every magnetic
bubble surface.

These easy paths are easy, though, because the atoms provide free
hops. Which means that the effective path length through space (where
energy is actually stored) is much shorter. This 'shortness' is what
the mu_r measures. The way I see this is that if you have a core
material with a typical permeability of 5000, then that means that the
vacuum portion in the typical lowest energy pathway through any
specific length of it is 5000 times shorter than what you'd measure
with a tape measure. Or, if you have 5 inches of the material, then
the iron atoms in it provide (5/5000) or 1/1000th of an inch of vacuum
that the magnetic field must cross over by force, with 4+999/1000ths
inches of free hops across iron atoms. This is why I spoke earlier
about my imagination regarding why very high permeability materials
tend to also be conductive, as well. On the other hand, there are low
perm materials (typically in the low hundreds, so let's use a figure
of 250) where you'd get (5/250) or 1/50th of an inch of vacuum and 4+
49/50ths of free hops. In that case, there is enough "binder" in the
material to separate bits of iron and keep conduction down, while
mostly providing a shorter pathway. It's a trade-off.

Another aspect in these iron cores is eddy currents. These are kind
of like "electron dogs chasing their tails." Any current flow through
the coil induces a magnetic field. But then this magnetic field
permeates the area around it (and especially through the iron core
because of the easy pathway there.) But just as electron motion sets
up a magnetic field, it's also true that any magnetic motion also sets
up an electric field. And if there are electrons available in the
conduction band (electrons that belong to atoms but where they are
just barely attached to the atoms, unlike valence electrons which are
firmly held) of atoms where such electric field potentials are set up,
they start moving away from the negative potential end and towards the
more positive potential, if they can. Iron has lots of electrons in
the conduction band, so those electrons want to start moving. If all
there is _is_ more iron, then they can move and they do. With very
low rates of change in the magnetic field, the electric potentials
that are set up are very small and so the electrons do not accelerate
very fast and they also have a lot of time to move, as well. All this
just means that not very much energy is wasted moving them around
(work is force times distance and although they have time to travel
some distance there, the force is very very small and the total work
is tiny.) When the current through the coil oscillates back and forth
fast enough, though, a very strong electric field is also set up and
the electrons accelerate quickly. Of course, the field changes
quickly, too, and reverses their motion soon after. So the electrons
start running around in tiny circles (they'd collide too much if they
went in straight lines back and forth, so to avoid that effect they
quickly arrange themselves in 'traffic' loops.) That is, if there is
a free conduction path for them to do so. If you powder up the iron
enough, into bits that are even smaller than the natural loops these
electrons would form into, and bind them back together with something
that isn't conductive at all, then despite the strong electric field
they cannot really move very far. They still move, but then they run
up against a barrier and sit and wait for the field to change and go
the other way in their tiny little cage. This greatly shortens the
net distance they can travel in and despite the strong force their
travel distance is forced to be smaller than they'd otherwise do. So
the net force times distance shrinks down and the wasted energy in the
core is less.

I suppose an optimal core for eddy currents (higher frequencies in the
magnetic field induce higher electric potential forces) might set an
iron atom forced somehow to be isolated by enough distance that the
electrons wouldn't travel across the gap for any particular electric
potential (this means separating them further and further apart for
higher and higher frequencies.) [Note: This gap might be created by
the use of atoms that won't conduct, though their very presence would
probably mean more distance is required between the iron atoms.]
However, this increasing gap distance would require the magnetic field
to place energy in it to hop across, so the iron atoms would represent
less and less of a free hop as a net percent of the total distance and
eventually you'd be almost as well off with just a vacuum in terms of
total size of your inductor.

Getting back to equation (1) and equation (2):

(1) L = mu_0 * mu_r * N^2 * A_e / l_e
(2) L = mu_0 * N^2 * A_e / l_e

Let's assume that all the energy goes into the vacuum, only. We
measure, at our macro scale with a tape measure, a loop length (l_e)
of 1 and a cross section area (A_e) of 1 and use N=1. But there are
two such inductors. One with a true vacuum only, one with an iron
core of permeability mu_r=5000. If we used equation (2) on our air
core, we get the right figure. But if we used equation (2) on our
iron core, we don't because actually all those iron atoms are
occupying most of the l_e that we had measured. In fact, 4999/5000ths
of it. So the effective l_e that we should have used would have been
1/5000th of what we earlier tried to use and where we got the wrong
resulting value for L. So, to compensate for this, we introduce mu_r
as a compensating factor. Since l_e in the denominator was 5000 times
too large, due to the fact that our measurements included a lot of
iron atoms along with the tiny bits of vacuum, then we need to add a
term in the numerator that is 5000 to compensate for using a number
that was 5000 times too big in the denominator. Doing that 'fixes'
the result. But it remains that it is only the vacuum, not the iron,
where all that energy gets placed.

Does that make sense?

Jon
.

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