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

["Rauber, Joel" <Joel.Rauber@SDSTATE.EDU>]

John,

You find the energy argument to be unnecessary and non-constructive; but do you find it invalid?  Your executive summary seems to imply "no" to the question of validity to the energy alone argument. 

 However further down, where you refer to "covering all the bases" as necessary for a "contrafactual" argument; you suggest that the energy argument alone does not suffice; from which I infer a response of "yes" to the validity of the energy argument (since all the bases aren't covered).

Joel Rauber

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Thursday, April 03, 2014 6:01 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Lenz's law and conservation of energy

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.
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