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

[John Denker <jsd@av8n.com>]

As a general principle, it is better to emphasize
stuff that is correct, rather than making a fuss over 
stuff that is incorrect.  In that spirit, here's how 
I understand the sign that appears in Lenz's law:
It is what it is, because of certain positive and 
negative signs that appear in the Maxwell equations 
and in Ohm's law.

If you want a mnemonic, think of a perfect conductor,
which excludes and/or traps magnetic flux entirely.
(This is not to be confused with a /super/ conductor
which actively expels flux, via the Meissner effect.)
A less-than-perfect conductor excludes and/or traps
flux temporarily.  Also, the existence of the term
"skin depth" tells you the sign of the effect.

This is not as sexy as pretending to figure out the
sign based on deep energy considerations ... but it
is more correct.  Maybe there is some deep principle
involved, but I doubt it, because deep principles
don't have exceptions, and the existence of para-
magnetism proves that laws similar to Lenz's law
*can* exist with the opposite sign.

I don't like the "energy argument" even as a mnemonic,
because AFAICT is it just wrong physics.


On 04/01/2014 08:37 AM, andre adler quoted from the book:

> "Lenz's law is also directly related to energy conservation.If the induced
> current in Example 29.6 were in the direction opposite to that given by
> Lenz's law, the magnetic force on the rod would accelerate it to
> ever-increasing speed with no external energy source, even though electric
> energy is being dissipated in the circuit. This would be a clear violation
> of energy conservation and doesn't happen in nature."

Maybe there's something I'm not seeing, but that looks
wrong to me, and I don't see any way to fix it.

By way of background, people tend to be very confused
about the concepts of /equilibrium/ and /stability/
... neither of which is the same as /conservation/ of
energy.  Here is how I explain equilibrium and stability:
  http://www.av8n.com/how/htm/equilib.html

It seems to me that the passage quoted above is essentially
making a /stability/ argument.

At this point we have at least three problems:
  a) (minor) The stability argument is being wrongly
   described as a conservation argument.
  b) There is no law of physics that requires physical
   systems to be stable!  For example, a uniform distribution
   of interstellar gas is not a stable situation.  It is
   unstable against condensation into stars and galaxies.
  c) There are situations closely (albeit not exactly)
   analogous to Lenz's law where the sign is backwards.
   I'm talking about paramagnetism.  This *does* occur
   in nature.  This does not violate conservation of energy
   ... and secondly, usually, it does not even lead to 
   instability when an external field is applied to a
   paramagnet.

   *Sometimes* if you have a bunch of paramagnets in a
   box, *provided* the interaction is strong enough,
   it can lead to instability.  We have a name for this:
   runaway paramagnetism is called /ferromagnetism/.


On 04/01/2014 09:16 AM, Jeffrey Schnick wrote:

> It seems to me that you would always have a runaway effect.

Sure, there are situations where you /can/ have instability.

However, this still does not mean that the energy argument,
as usually stated, makes sense.  There are lots of unstable
situations in this world, and they do not violate conservation
of energy.

There are treeeemendous amounts of confusion about this 
topic.  Chemists have even elevated the wrong answer to the 
status of a "principle", namely Le Châtelier's principle.
Prof. Le Châtelier stated his "principle" in a couple of
different ways, one of which is wrong, and the other of
which is trivial:
  a) All chemical equilibria are /stable/.
  b) All stable chemical equilibria are stable.

In any case, one key to maintaining your sanity when such
things are being discussed is to remember:
  equilibrium ≠ stability ≠ conservation of energy