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# Re: Lenz's Law

• From: "John S. Denker" <jsd@MONMOUTH.COM>
• Date: Thu, 7 Jun 2001 06:33:43 -0400

At 02:37 PM 6/7/01 +1000, Peter Craft wrote:
a recent advice document circulated around our schools suggested an
anology could and should be made between Newton's Third Law of Motion and
Lenz's Law.

I'm never quite happy calling it "Lenz's Law". I'd rather call it "Lenz's
tendency", because it is such a limited and inexact rule. Although there's
nothing wrong with inexact laws (most of our laws are inexact if you look
closely enough) my point is that Lenz's "law" is a lot lower on the totem
pole than Newton's third law.

Newton's third law is related to conservation of momentum. This is one of
the most profound and quantitative laws of physics. It applies to all
three components of momentum, for all objects big or small, red or green or
purple.

Lenz's "law" is related to the conservation of flux. It constrains only
one component of the magnetic field; the two components parallel to the
surface are unconstrained. There is real conservation only for type-I
superconductors, not for type-II superconductors and certainly not for
ordinary non-super conductors. There is no conservation for
non-conductors. There is no practical conservation even for conducting
materials, if the material is sliced in to thin mutually-insulated sheets.

As applied to an ordinary chunk of metal, Lenz's tendency gives a rule of
thumb as to the sign of the initial (short-term) effect. For times greater
than t=0, there is no quantitative prediction. In contrast, Newton's law
makes a highly quantitative prediction for all time.

Conservation of momentum is the most convenient and reliable way to
remember a powerful concept. In contrast, I find Lenz's tendency to be
much less convenient and much less reliable than a direct appeal to the
Maxwell equation (V = phi dot) and Ohm's law.

A "law" that gives me only one bit (the _sign_ of the initial effect) is
pretty small potatoes compared to the power and grandeur and precision of
conservation of momentum.

I would say that the concepts are
-- in some ways analogous, but
-- in many ways not analogous.

It seems misleading to say "an analogy could and should be made" without
detailing how severely limited the analogy is.