Re: [Phys-L] Lenz's law and conservation of energy

[John Denker <jsd@av8n.com>]

Executive summary:  I still find the energy argument to be
unnecessary ... and also non-constructive.  The constructive
calculation based on V = flux_dot and V = IR works just fine.
Here I mean "constructive" as in "constructive proof" as 
opposed to proof by contradiction.  In particular, the
constructive calculation provides far more insight as to
what happens for zero resistivity, low resistivity, high 
resistivity, and everything in between ... whereas the
proof by contradiction doesn't give you much more than the
sign of the effect.  So again this is a 100% solid physics
reason *and* a pedagogical reason to prefer the V = flux_dot
and V = IR approach.

On 04/03/2014 02:17 PM, Philip Keller wrote:
> Similarly, if I drop a magnet down an aluminum tube (commercially
> sold as a Lenz's Law Apparatus), the induced currents flow to as to
> inhibit the fall.  As the magnet drops, much of the lost potential
> energy is converted to heat as current flows in loops around the
> tube.  If the current were to flow in the direction that sped the
> fall of the magnet, how would we account for the greater energy?

You make one of my arguments for me!

The opposite of heating is cooling.  If we are going to
hypothesize the opposite of Lenz's law, then the magnet 
accelerates and the tube cools down as it does work against
the magnet.  This is analogous to an ideal gas that cools
as it expands, doing work against a piston.

Presumably your intuition says that the tube does not behave
this way, and in fact your intuition is correct, but it
cannot be based on an energy argument alone.  It has to 
include an entropy argument also.  Cooling the tube would 
violate the second law (not the first law).  Furthermore,
this needs to be a somewhat detailed argument, since if 
the tube were a gas rather than a metal, it would be 
possible for it to give up some of its energy by cooling.

This is necessarily a tricky discussion, because it deals
in contrafactuals.  It follows the same form as a proof
by contradiction, which is always tricky.  To make it
work, you have to cover /all/ the bases.
 -- If you assume the second law always holds, you can
  explain the contrafactual result as a violation of
  the first law, as Jeffrey Schnick pointed out.
 -- If you assume that the first law always holds, you
  can explain the contrafactual result as a violation
  of the second law.
 -- Or you could have a situation where both the first
  law and the second law are upheld, but the system is
  simply unstable (e.g. interstellar dust, or tray of 
  magnets).
 ++ In general, you have to cover all the bases.

So I'm not saying that the energy argument has no place
in the analysis;  I'm saying that it does not suffice 
by itself.  It leaves too many bases uncovered.

> it sounds like you are disagreeing on pedagogy and not with the physics

I wouldn't have said that.  It seems to me that entropy 
is not the same as energy, and IMHO this is exceedingly 
fundamental physics.  Also the rule that says you have
to cover all the bases is IMHO an ultra-fundamental
principle of logic.

Furthermore, I see the physics and the pedagogy as so
intimately intertwined that it is hard to make progress
on one without the other.  In particular, I always see
/connections/ as important ... important to students'
understanding, and therefore important to teaching, but
also important to my own understanding, whether I'm
teaching or not.

In this spirit, I see the connection between Lenz's law
and Ohm's law to be significant.  If we understand the
sign in Ohm's law, we get the sign in Lenz's law almost
for free.  Furthermore, the application to Ohm's law, 
and the reasoning behind it, is 1000 times more broadly 
useful than is the specific application to Lenz's law.
Is this a pedagogical argument?  I suppose so, but it 
is also a 100% solid physics argument.

In particular, whether or not we have an explanation for
Lenz's law, we reeeeallly need an explanation for Ohm's
law, along with the more general idea of screening within
conductors.  It is nice to find that the same argument 
works for both.  This is an example of the unity and 
power and grandeur of physics.

> Your example with two masses is a different case, not just in the particulars.

You see the differences as important, but I don't.  I see
a strong chain of connections:

  Lenz's law --> Ohm's law --> Coulomb's law --> Gravitation.

If there were a valid energy-only argument here, it would
work at the level of Coulomb's law ... and would also work
for gravitation, which it doesn't.

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

In any case I still find the energy argument spectacularly
unnecessary ... and also non-constructive.  The constructive
calculation based on V = flux_dot and V = IR works just fine.
Here I mean "constructive" as in "constructive proof" as 
opposed to proof by contradiction.  In particular, the
constructive calculation provides far more insight as to
what happens for zero resistivity, low resistivity, high 
resistivity, and everything in between ... whereas the
proof by contradiction doesn't give you much more than the
sign of the effect.  So again this is a 100% solid physics
reason *and* a pedagogical reason to prefer the V = flux_dot
and V = IR approach.

  Pedagogically speaking, this provides an opportunity to
  review the Maxwell equations and review Ohm's law, to
  make a point about their wide utility.  Save the energy
  argument for another day, for a situation where it can
  be applied more directly.

  This is also an opportunity to review Kirchhoff's so-called
  laws, and to point out the the loop law gives 100% the wrong
  answer in this situation.