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



Now that's what I call a good, solid argument for this case.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Moses
Fayngold
Sent: Friday, April 04, 2014 10:58 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] Lenz's law and conservation of energy

On Thursday, April 3, 2014 11:29 AM, Philip Keller
<pkeller@holmdelschools.org> wrote:


"A u-shaped circuit is closed by a bar that can slide across the rails.
There is a magnetic field directed down into the plane of the rails.  I apply a
constant force to drag the bar to the right.  There are a number of ways to
predict the direction of the resulting current.  One of them is to say that the
increase in the enclosed flux due to the increased area of the loop must be
opposed by the outward field caused by the resulting counter-clockwise
current.

Is that not an example of Lenz's law?

And if the current were to flow in the direction opposite to that predicted by
Lenz's law, would I not get a current that would help me to drag the
bar?  Couldn't I then let go of the bar and let that induced current continue to
accelerate the bar for me, thus producing free energy?"

  My answer to the last question is: "No, you could not." And my argument
for it is as following:
1)  The actual direction of the current in the bar is predicted by the Lenz law.
But you could predict the same direction just from the Lorentz force law  F =
q V X B, without any other references. This means that at least in the
textbook example when the change of flux is due to motion of the bar in a
field B, the Lenz law is merely a corollary of the Lorentz force law.
2)  In this case, the change of sign in the Lenz law would be equivalent to
changing sign in the Lorentz force law
3)  That would indeed, change the direction of induced current; but by the
same token, the inverted current would now be subjected to the Lorentz
force law with the opposite sign. And the product (inverted current times the
inverted Lorentz force) would produce exactly the same outcome as before -
you would need to push the bar with the same force.
 Conclusion:  The necessary force applied to the bar and thereby the energy
input is insensitive to change of sign in the Lenz law.
  One could raise another question: change of sign in the Lenz law would
increase the magnetic field B within the loop. Will this not increase the
magnetic energy of the system? The answer is "No" because by the same
token it would decrease B outside the loop. Again, at least in the framework
of considered example, it is evident that positive and negative contributions
cancel each other, so that change of sign in the Lenz law would not affect the
net magnetic energy of the system, either.
  So my conclusion remains the same: the minus sign in the Lenz law has
nothing to do with energy conservation.

Moses Fayngold,
NJIT
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