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Re: Lenz 's Law



Here I'm probably going to illustrate (again?) how a little knowledge is
worse than none.

Using a mag. field to align formerly random, atoms reduces the entropy?
They are also now at a reduced energy. (the para case)

I'd appreciate a detailed analysis of this starting with the energy
required to "create" the initial mag. field.

How does this relate to the absorption from an EM field in EPR? Is the
absorption when the field "randomizes" the formerly aligned atoms? Or is
it precession, or?

bc

"John S. Denker" wrote:

Quoting Bob S, Bernard Cleyet wrote:

"1) The torque on a magnetic dipole (ex a circular current loop) due
to an externally sourced B field will tend to line up the dipole with
the instantaneous direction of that B field so that the dipole's B
field strengthens the original, external B field (inside the loop).
This can be seen as just the result of the qVxB force."

and this "takes" work, i.e. the magnetic material "contains" more
energy than before.

Actually, that last remark is exactly backwards.
A paramagnetic material in a field has a _lower_
potential energy than the same material in a
no-field region.

"2) A time varying B field generates an E field (Curl E = - dB/dt)
which will drive currents in accordance with Lenz's Law."

same ("takes" work).

with 1) this effect is non conservative (hysteresis) and result s in
conversion to an increase in it's (the material's) random internal
energy (ke + ).

2) same (except in a superconductor?)

A) The fact that a backwards energy factoid was
introduced to explain the behavior pretty
much proves my original point that the energy
principle isn't a reliable guide to which way
the Lenz's law current goes.

B) The unreliability of the energy argument seems
to me fundamental, not superficial.

If you have the Maxwell equation
del F = 4 pi J (help stamp out cross products!)
then you don't need the energy principle, and
the converse doesn't hold; given the energy
principle you still need the Maxwell equation.

As far as I can tell, the energy argument has
at least two problems. I don't see how to fix
one without running afoul of the other.

The first problem is that the original version
of the energy argument seemed to proceed from the
assumption that sticking a material, any material,
into an inductor will lower its inductance.
That's just not true; it depends on whether the
material is diamagnetic or paramagnetic.

The second problem is that energy is a scalar,
while the induced current is a bivector. It's not
easy for a scalar to tell you the direction of a
bivector. This is a symmetry argument. An argument
that fails a symmetry check is in severe trouble;
it's like failing a dimensional-analysis check.

You can say that the induced-current bivector is
aligned with the applied-field bivector, but is
it aligned or anti-aligned? You can't decide
whether alignment or anti-alignment has lower
energy until you know what material you've got,
and until somebody has analyzed the material
using a whole lot more than the energy principle.