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.