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[Phys-L] Ohm's law --> Lenz's law --> energy and/or entropy



Since people seem to be finding value in the recent
discussion, let me say a few more words.

A) Pedagogically speaking, when discussing Lenz's law
I would explain the sign by direct appeal to Ohm's
law plus Maxwell's equations. Closing a circuit
allows current to flow in a direction that reduces
the voltage. That means less flux_dot threading the
loop. At this level of detail, that's all one needs
to say.

This implicitly depends on the stability of Ohm's
law, which depends on the resistance being positive,
but IMHO it's not necessary or even helpful to bring
that up in this context. Most students will happily
assume that the resistance is positive. This assumption
can be questioned another day.

B) Indeed, most students will use Ohm's law 1000
times more often than Lenz's law, so I suggest we
shift our discussion to focus on Ohm's law. If we
understand the sign in Ohm's law, we get the sign
in Lenz's law almost for free.

C) By way of background, note that there is a distinction
between
1) A perpetual motion machine of the first kind, and
2) A perpetual motion machine of the second kind.

These are predicated, respectively on
1) A violation of the first law of thermodynamics
(conservation of energy), and
2) A violation of the second law of thermodynamics
(paraconservation of entropy).

D) A negative resistance in Ohm's law V = I R corresponds
to a negative dissipation in the Joule heating law
P = I^2 R.

Negative dissipation does not violate conservation of
energy, just as positive dissipation does not. OTOH
if we restrict attention to a simple *passive* wire
or chunk of metal, negative dissipation would violate
the *second* law of thermodynamics. There is not any
energy problem, but there is an entropy problem.

Tangential remark: More generally, for active circuits,
it is not particularly difficult to produce negative
resistance, and this does not violate the second law,
just as a refrigerator does not violate the second law
when it moves energy (and entropy) from a cold place
to a hot place.

====================

So ... As of today I am slightly more sympathetic to the
previous bogus "explanations" that people have cited.
The wrong explanations are still profoundly wrong, but
at least now I can see how somebody could come up with
the wrong explanation by a "normal" process of mutation,
without being completely crazy.

Specifically, I can almost see how somebody could correctly
identify a Lenz's law violation as a perpetual motion
machine, and then drop the ball when it comes to making
the distinction between the first law (energy) and the
second law (entropy). This is a ghastly mistake, but
not completely crazy.

Even then it's hard to make sense of the alleged "explanations"
because, as I said, it's bad luck to prove things that
aren't true, and unless you throw out the bogus explanations
entirely and start over, you are in danger of proving that
paramagnetism doesn't exist.

As a useful rule of thumb, fundamental questions about
equilibrium, stability, reversibility, and spontaneity
require answers in terms of entropy. *Sometimes* under
special conditions you can use the energy of the system
as a convenient /proxy/ for the entropy of the world, but
this cannot be taken for granted. For details on how this
works, see
http://www.av8n.com/physics/thermo/spontaneous.html
especially
http://www.av8n.com/physics/thermo/spontaneous.html#sec-analysis

=================

Final tangential remark: It just amazes me how many
femtollectuals there are who insist on crossing out every
occurrence of the word "voltage" and replacing it with
"potential". Well, the Lenz's law situation is a fine
example of a situation where the voltage is *not* a
potential.

Voltage is voltage, and is properly called voltage.
Sometimes the voltage is a potential and sometimes it
isn't. Ohm's law applies just fine to non-potential
voltages. For details, see e.g.
http://www.av8n.com/physics/voltage-intro.htm
http://www.av8n.com/physics/kirchhoff-circuit-laws.htm#sec-mesh