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Re: Earth's Magnetic Field



On Tue, 13 Jul 1999, paul o johnson wrote:

William Beaty wrote:

The computer simulations in that SciAm article depict the motion as a big
nasty mess of 3D vortices. Imagine a hot-tub with several turbulent water
jets. Imagine a bunch of smoke-rings which are colliding and
interweaving.

In which the water is moving relative to the tub and the smoke is moving relative
to the floor. So the Earth's fluid outer core is moving relative to what?

I don't understand your question. Are you assuming that we could choose
an inertial frame in which the molten iron was NOT moving? A roiling
liquid is like a collection of flywheels having a variety of orientations.
If I claim that those flywheels were spinning, I don't need to say what
their motion is relative to. It's relative to the other flywheels in the
group. Relative to any inertial frame. If the water in a bathtub is in
complicated swirling motion, we don't need to look at the walls of the tub
in order to see that this is so.


A Wimshurst electrostatic generator gives a good analogy: if there are no
ambient e-fields present, then the Wimshurst generator will never develop
a high voltage no matter how long we turn the crank. But if a small
e-field hits the device, it causes a breaking of symmetry and the machine
can then ramp up its voltage exponentially until it is limited by corona
leakage. A shorted-out self-exciting dynamo is similar: we can crank it
forever, but if there is zero ambient b-field, then the generator won't
run. If a small ambient b-field is present, then the generator can create
a small current, which makes a bigger b-field, which generates a larger
current, and the current grows exponentially until it is limited by
resistive losses.

And to hell with Lenz's law, huh?

Please bear with me, William; your explanations are slowly opening the door to
understanding for me. But each answer generates further questions.

Hey, I love having to answer questions, since it usually forces me to
undergo "aha" experiences which were waiting in the wings.

I see your point. Like the Wimshurst machine, our "Earth Dynamo" needs to
be cranked while the above effects are occurring. If the center of the
core is hotter, and hot liquid iron is rising in plumes because of
bouyancy, then there is a heat-engine turning the "rotors" in the dynamos.
The dynamos must act like parasites which feed on the temperature-driven
convection flows and slow them down. This would be very similar to the
electromagnetic braking forces seen when mercury is placed in a strong
magnetic field and then stirred. However, it would be very weird if we
could stir the mercury and then remove the magnet, and have the mercury
keep supplying its own magnetic field as long as we kept stirring it. If
the metal was molten iron rather than mercury, this might actually occur,
although it might not be possible to stir it hard enough in a real-world
experiment. But if the pot of liquid metal was large enough, its internal
dynamos could be kept spinning simply by heating the bottom and cooling
the top.

The Earth's dynamos act like shorted-out generators. The moving
conductors are the only electrical load. I think it's appropriate to
imagine that the resistance of the liquid iron is very close to zero.
Over short time scales conductors can act like perfect conductors. Bring
a magnet *instantly* up to a copper plate, and the copper plate is
repelled as if it was a superconductor. If the motions in the liquid iron
occur over a time scale which is far shorter than the L/R time constant of
the current loops within the iron, then the the liquid iron acts somewhat
like a perfect conductor. Any lines of b-field which happen to penetrate
the iron will be dragged along as it moves. If the swirling iron causes
the lines of b-field to stretch, then electric current is increasing and
EM energy is being created, so we should expect a counterforce to arise
which slows the moving metal.

Hey, there's another way to see it: as long as we keep stretching and
folding the masses of b-field "fibers" that are trapped in the liquid
iron, we can keep the dynamo operating. It takes work to do this.


I wonder what the time-constants are like in the core? The Exploratorium
had a small exhibit on the time-constant of a small, thick aluminum ring.
With a laminated iron ring wrapped through the hole in the aluminum ring
to act as an inductor core, the time constant was a couple of seconds. If
the entire thing was a few million times bigger, it would approach the
scale of the hundreds-km flux regions in the Earth's core. If all the
linear dimensions of an iron-core inductor are doubled, doesn't the series
resistance decrease by half, yet the inductance doubles? If that's right,
then the L/R of a ring of flux trapped in the Earth's core might be
roughly 10^13 times longer than a few seconds.



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William J. Beaty SCIENCE HOBBYIST website
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