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Re: corrupting the youth



So in classical physics I'm not allowed to view a magnetized
needle as a 1-dimensional object? I have to get down and view it on an
atomic scale (the magnetism comes from the atoms which line up their
moments)? If this is the view that I'm asked to take I think that we've
reached the point of the dialogue where we can just agree to disagree.
I do, however, have some remarks about the mathematics.
Maybe I'm missing something subtle, but it seems to me that John
is making a firm prediction that magnetic monopoles cannot exist.
If there are magnetic monopoles then there is a complete symmetry
between electricity and magnetism and you must flip a coin to decide which
one should be described by a surface and which one should be described by
lines of force (a vector field).
Further, on aesthetic grounds, a description of the process of
mapping out magnetic field lines with a compass needle becomes
indescribably ugly and painful to describe. And, for heaven sakes, get
rid of those lecture demos where you show magnetic field lines with iron
filings!
Regards,
Jack


On Sun, 1 Sep 2002, John S. Denker wrote:

Jack Uretsky wrote:

Please share your insight. I lay a loop of wire carrying
current on a table. A magnetized needle is placed inside the loop. This
is all in two dimensions. Now make a picture, without invoking a third
dimension, of the forces and/or torques acting on the needle.

As I have mentioned before, recently and otherwise,
there was once a kid named Pierre who was fascinated
by this problem.

For a diagram and other details, see
http://lists.nau.edu/cgi-bin/wa?A2=ind0104&L=phys-l&P=R2423

Dealing with Jack's question requires noticing that the
question is ill-posed. The initial setup is not nearly
as symmetric as it is purported to be.

Compass needles are not one-dimensional abstractions.
In effect they have chiral belts around their fat
middles, and the markings on the belts say "my magnetic
bivector circulates that-a-way".

If you don't visualize this belt, you will misunderstand
the symmetry of the system. You'll have a paradox on
your hands. (If you don't see the original (mis)statement
of the problem to be paradoxical, i.e. if you really
think the set-up has reflection symmetry in the plane,
then you really don't understand the symmetry of the
physics of electromagnetism.)

If you do visualize this belt, you can add the magnetic
bivector of the macroscopic current loop (which lies in
the plane) to the bivector of the belt (which is not in
the plane) using geometric and physical techniques as
illustrated in this figure
http://www.monmouth.com/~jsd/physics/gif48/add-bivectors.gif
or the equivalent mathematics (Clifford Algebra).

Cross products are neither necessary nor helpful for
this. Cross products are IMHO misleading, because they
might allow someone to think that the original problem
was symmetric, and the symmetry was somehow broken by
application of the RH rule when the current was turned
on. This would be just totally wrong physics.


--
"What did Barrow's lectures contain? Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings. (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
V. I. Arnol'd in
Huygens & Barrow, Newton & Hooke