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Re: motional emf



Kenny Stephens wrote:

The text says that each charge carrier, q, in the rod has the
velocity v and since q moves in a magnetic field it experiences a
lorentz force F_M= qv cross B. The text then states that the work
done by this force pushing the charges along the rod is F_M * L=
qvBL. Since emf is energy per charge, the motional emf between the
ends of the rod is E= vBL.
...
I prefer the explanation of calculating the changing flux, Phi_M=
BLx, through the circuit where x is the position of the rod measured
along the rails from the resistance. This gives the emf E=
-dPhi_M/dt= BL(dx/dt)= BLv.

After all this yacking, my reason for posting is to get a range of
opinions of this text's derivation.

There is a Maxwell equation that tells us
voltage = flux dot
and applies when we have a changing flux in a given loop.
It does *not* necessarily apply when we have a flux that
sits there while the loop changes. Counterexamples abound.
It turns out that this situation is not a counterexample,
i.e. the result (E=vBL) is OK in this situation. IMHO the
"flux" derivation given above does not really prove or
explain the result.

As Hugh pointed out, the reliable physically-sound flux
calculation calls for transforming into the frame of the
wire, figuring out what is going on in that frame, and then
transforming back to the lab frame. Alas that procedure
may not be much help because it uses concepts (i.e.
relativity) that probably haven't been covered at this
point in the book, and concepts (i.e. transforming the
*fields*) that may not be covered in an intro book
at all.

The Lorentz-force argument in the book looks OK to me.

> Now this bugs the heck out me because magnetic forces are not
> supposed to do work.

That's a weak argument, because magnetic forces are not
the only forces involved. There are also the forces that
constrain the charges to remain inside the wire. (Some
students may be puzzled by this, too, because they've heard
a rule that says constraints are not supposed to do work
... but that rule only applies to nonmoving constraints;
we can easily do work using a *moving* constraint.)

Also work arguments don't count as an argument favoring
the flux approach over the Lorentz-force approach; work
arguments should apply equally to both approaches.

It may be illuminating to calculate how much force is
required to move the wire, and to look closely at the
physical processes involved.