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I'm currently reviewing some chapters for a "well-known" cal-based
intro physics book. It uses a popular explanation (I've seen it
elsewhere) for deriving the emf developed by a conductor moving with
uniform velocity through a constant magnetic field. Jsut to be
thorough, here's the setup:
Two conducting rods are placed parallel to each other. Let's call
them rails and say the left end of both rails are connected by a
resistance, R. Another conducting rod of length L is placed across
(perpendicular) to the rods and can slide freely along the rails. An
external agent acts on the rod to give it a uniform velocity, v,
parallel to the rails (and away from the resistance). A uniform
magnetic field is applied perpendicular to the plane of the problem
(let's say into the page). Assume a current flows through the
circuit (through R, along one rail, up the rod and returns along the
other rail) such that the charge carries have a drift velocity v_d.
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.
Now this bugs the heck out me because magnetic forces are not
supposed to do work. Using this explanation just sets the students
up for confusion and puts me in a pickle to try to justify it.
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.