Re: corrupting the youth

["John S. Denker" <jsd@MONMOUTH.COM>]

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.