Re: magnetism question


<muknot@xxxxxxxxx> wrote in message
news:1134445687.108960.206730@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hi, thanks for all the replies. What i still don't understand is why
> the flux leakes. One of the replies said that the additional flux in
> the iron is due to the iron becoming magnetized -- that's fine, i
> understand that. But how does this explain the fact that the flux
> leakes out of the iron if you remove a pit from the surface of the iron
> sample if the iron is at saturation. Why isn't the flux distribution
> the same as before the iron had a pit in it?

Why does the flux need to
> take up more volume in air

Well, the integral of H dot B might explain this.

(since it leakes outside the sample where
> the pit is, it takes up more volume).

Why is it that there is far less
> leakage if the iron is below saturation?

Possibly, because below saturation a generally low H results in the bar
magnet's energy being mostly accounted for within the iron while surrounding
air regions won't account for much of it. With generally low H everywhere
you would describe the situation as 'little leakage flux'. Beyond
saturation, H everywhere probably has to rise significantly until the bar
magnet's energy is accounted for. With increasing H everywehre, you would
probably describe it as 'increasing leakage flux'.

After all saturation is just
> the point where all the domains are aligned with the field. I think an
> equivalent quesion would be, why do magnetic fields fringe in the air
> gap of a core as shown in http://leeh.ee.tut.fi/transformer/tra11.htm.
> Is there a simple explanation for this, or was it already offered and i
> missed it? Thanks again.
>

The easy answer, though least satisfying, is to get used to it. Often
discontinuities result in these sorts of effects. You have probably seen it
before, e.g. electric field at the perimeter of a capacitor plate. It would
boil down to some field equations, differential equations, and similar nasty
stuff. You will probably get a feel for when things will and will not
behave like this.

Another thing to keep in mind is that there are paths through the air which
go from the North to the South poles, so there will be flux in the air along
those paths.

Maybe the reason for the apparent preference of an iron path is energy
related. I think a small H will result in large B inside your iron and that
the small volume of iron can account for a lot of the bar magnet's magnetic
energy (energy, I still believe, is proportional to H dot B over the
volume). So consider a solution for the magnetic fields with just the bar
magnet in air. There will be a moderate H and a moderate B streaming about,
and there will be some value for the integral of H dot B, relating to the
energy of the bar magnet's magnetic field. Now put iron near the bar
magnet. If the H everywhere stayed the same, the B inside the region of
iron would increase versus air and this would imply an increase in energy
(increase in the H dot B integral). Let's assume this is not valid. Let's
assume the H everywhere will generally decrease, to an extent such that the
integral of H dot B is the same before and after locating the iron close to
the magnet (for the moment). We generally expect H to go down and B (and
therefore flux) in the air to decrease. Now the integral of H dot B
throughout the air region is lower and represents less magnetic energy. In
the region that used to contain air but now contains iron, the H may be
lower but the B much higher, so the integral of H dot B in that region is
higher and represents more magnetic energy than that region used to account
for. So energy is about equal before and after moving the piece of iron
near the magnet. And we see flux in the air surrounding the iron decrease
while flux in the iron becomes large. This would describe the apparent
affinity for an iron path. There's one more energy effect that I think
should happen. Moving the iron close to the magnet should decrease the
magnetic energy of the bar magnet. I say this because it takes energy to
move iron away from a bar magnet, and presumably the energy goes into the
magnetic field because the magnetic field would be able to pull the iron
back. So vice versa should apply. The point is, having the iron nearby is
a configuration of lower magnetic energy and I think Nature is happy to have
less energy stored in magnetic fields. Got all that? If so, don't forget
to take it with a few one kilogram grains of salt. It might be all hooey.
Anyways, removing a pit from the iron surface requires a new field
configuration that presumably should account for all of the bar magnet's
magnetic energy. And which must satisfy all the field equations and all the
applicable conceptual shortcuts we use. Why would the flux do some fringing
at the pit? Maybe the surface current concept explains that tendency.
Maybe not. Give it some thought.

j


.

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