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Re: [Phys-l] a magnetic filament snapped.



Chuck Britton wrote:
from http://spaceweather.com/ (a nasa site) I read:

Yesterday on the sun, a magnetic filament snapped.

I would like to think that some of my sharp HS students might wonder
about the 'basic physics' involved here.

A reasonable question.

I like to visualize 'lines of magnetic flux' as Faraday did.

There's no harm in that, in the nonrelativistic limit.

Basic physics says that these flux lines have no ends - so how can they 'snap'?

Here's a picture:
http://www.av8n.com/physics/img48/vortex-interaction.png

There are four snapshots of the same system. At time A, there is one
loop. Going from A to B, I flip the bottom of the loop, reversing the
direction of the green arrow in this projection. The result is a
figure-8 loop, with a crossing at the middle.

However, a loop with a crossing is the same as two loops touching at
a point. At time C, the two loops have moved slightly apart.

Going from C to D, I flip the bottom loop, so it has the same orientation
as it did at time A.

In this way, a big loop can be "snapped" into two smaller loops. Indeed,
if you twist a loop into a figure-8, it is almost guaranteed to "snap",
because C is energetically more favorable than B.

This sort of thing happens all the time in fluid dynamics, where the loop
is a _vortex line_. Such vortex lines are necessarily endless, for much
the same reason that magnetic field lines are endless: div curl x == 0
for all x.


(WWFS - What Would Feynmann Say?)

1) See volume II chapters 40 and 41.

2) Once upon a time, circa 1972, I asked Feynman what he would do if he were
starting his career over at that time. He said he would /not/ go into particle
physics at that time, because the field had been so thoroughly worked over that
the remaing questions were too far removed from any foreseeable application on
any reasonable timescale. He said he might go into fluid dynamics, because in
that area there were plenty of problems that were worth solving, but hadn't
been solved yet.

There are other folks with similar opinions: The Clay Mathematics Institute
lists some basic properties of the Navier-Stokes equation among a handful of
"millenium problems".
http://www.claymath.org/millennium/Navier-Stokes_Equations/


Ludwik Kowalski wrote:
I am imagining a beam of magnetic lines along which protons are
spiraling up, against gravity. Suppose the protons are suddenly "blow
away" by something. The magnetic loop is still in existence, but
without material particles in it.

That's not very likely. These magnetic lines are so strong that protons (or
any other charged particles) are pretty well "stuck" to the lines. Small
cyclotron orbits.