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



First, some possibly-helpful remarks:

My favorite demonstration of Lenz's law is the "jumping
ring" demo.
http://www.rpi.edu/dept/phys/Dept2/physlabsite/demoFaradayjumpingring.htm

Advantages include
-- There is no doubt that it demonstrates Lenz's law,
namely it verifies the /sign/ of the induced current.
The sign is such that the ring moves /away/ from the
high-field region.
-- All the important parts are out where you can see
them.

===========

Another favorite demo works great for "department open
house" events. It depends on having a huge, strong
electromagnet, perhaps something like this:
http://www.av8n.com/physics/img48/electromagnet-photo.jpg
You won't find such things in the typical high school,
but universities sometimes have them lying around.

Then make a thing that looks sorta like a hammer, with a
light but stiff plastic or wooden handle, and a symmetrical
head made of thick-wall copper tubing, of a size that will
fit between the poles of the magnet. The axis of the tube
is perpendicular to the axis of the handle, as diagrammed
here:
http://www.av8n.com/physics/img48/lenz-eddy-demo-ring-handle.png

A hollow tube is preferable to a solid chunk of metal,
because the eddy current effects scale like the enclosed
area, so metal near the axis contributes to the weight
without contributing much to the desired effect.

Use OFHC copper, i.e. oxygen-free high-conductivity copper.
Cool it by soaking it in liquid nitrogen. This increases
the conductivity by a factor of 4, which is quite noticeable.

Observe the force required to move the copper from far
away into the gap of the magnet.

Observe the force (or lack thereof) required to wave the
copper around within the region of uniform field.

Observe the huge torque required to rapidly flip the copper
end-over-end by twisting the handle.

In particular, with the copper not in the field, demonstrate
the desired rapid flipping motion, by spinning the thing
around the axis of the handle. Demonstrate putting the
thing into the gap and waving it around without spinning.
It's easy. Then hand it to a visitor. Let them practice
spinning it outside the magnet. Then tell them to put
it into the magnet and spin it /rapidly/. The effect is
huge. It takes a huge torque to produce even a slow flip.

Also notice that the effect is a torque proportional
to angular velocity. The force is not even remotely
proportional to acceleration, so this is a case where
the second law of motion cannot be applied, not directly
anyway.

After a few flips you will need to soak it in nitrogen
again, because the eddy current heating raises the
temperature quite a bit.

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

On 04/04/2014 04:47 AM, Philip Keller wrote:
So after I drop the magnet down the tube, say I present my energy argument.
Then a student asks "How do you know that the current in the tube couldn't
cool the tube?" ...

If so, I see that I do have to use the second law now. I know that the
tube doesn't cool the same way I know that room-temperature soda cannot be
made to levitate using energy that comes from cooling the soda.

Exactly so. That is the correct answer to the student's
question.

Is that the base that I've left uncovered?

That's a start.

The tricky thing about a proof-by-contradiction is that
you have to cover *ALL* the bases. Certainly the first
and second laws of thermodynamics are the #1 and #2
biggest bases, but there are so many screwy aspects to
the magnet-in-tube demo that it's hard to get a handle
on them all. Here are two more bases that come to mind:

Base #3: This probably applies to any analysis that
uses the energy argument to "derive" the sign of the
induced current, i.e. to derive Lenz's law. Suppose
that instead of an intact aluminum ring, we use a
ring with a small slit in it, like a C that is almost
closed, and make it out of magnetically iron. Then
(if you engineer things right) it will be /attracted/
to the core of the apparatus! There are all kinds of
industrial electromagnets that rely on this effect.
http://static.ddmcdn.com/gif/electromagnets-1.jpg
http://img1.photographersdirect.com/img/8998/wm/pd782367.jpg

This tells me that the "energy" argument was completely
bankrupt from the git-go.
-- The induced magnetism in the aluminum thing is
opposed to the applied field.
-- The induced magnetism in the iron thing is aligned
with the applied field.

Neither one of these effects violates conservation of
energy. You could get Lenz's law completely backwards
and still not violate the first *or* second law of
thermodynamics.

For now, I leave it as a puzzle for you: Where does
the energy come from when the iron is attracted to
the magnet?

Base #4: This applies to the magnet-in-tube demo, but
not necessarily to other demos.

Note that the jumping-ring apparatus can be used to
illustrate a second phenomenon, namely eddy current
heating. Ask a student to /hold/ the ring so that it
doesn't jump up. They can't do it, even though the force
is rather small. They can't do it, because the ring gets
hot!

I don't want to get unduly nitpicky about this, but as I
see it, eddy current heating by itself is *not* a valid
demonstration of Lenz's law. That's because if the sign
of the induced current were reversed, the ring would still
get just as hot. The ring would not jump up, and instead
would be /attracted/ to the high-field region ... but it
would still get hot. The heating goes like I^2 R, and
squaring the current makes the result completely insensitive
to Lenz's law, which by definition is a statement about the
/sign/ of the current.

Ditto for the magnet-in-tube demo. You could get Lenz's
law completely backwards and still have more-or-less the
same amount of eddy current damping.

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

Here's how I put the ingredients together:

1) If you start out by covering base #1, you have a
problem with entropy, which is fixable.
12) If you cover base #1 and base #2, you still have
a problem with eddy current heating, which is fixable,
perhaps by switching to a different demo.
124) If you cover bases #1, #2, and #4, you still have
a problem with paramagnetism. I don't see how to fix
this. Maybe some smart person can fix it, but so far
I haven't been able to come anywhere close. All of the
energy arguments (and entropy arguments) made so far
apply equally to diamagnetism and paramagnetism, so
AFAICT they could get diametrically the wrong sign in
Lenz's law and nobody would know the difference.
*) At this point, even if the energy argument wins you
lose, because the argument is so complex that it's not
worth bothering with, especially in the introductory
class, especially since there are easier and /better/
ways of getting the right answer. V = flux_dot and
V = I R taken together tell you *more* than Lenz's law
ever could.

Also V = flux_dot and E_dot = V^2 / R give you eddy
current heating. Obviously V^2 / R is partially related
to I R, but it is also different in important ways.