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Re: motional emf



Kenny Stephens wrote:

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.

I recently reviewed the derivations of the formula for motional emf.
You will find a brief write-up of what I uncovered here:

http://usna.edu/Users/physics/mungan/Scholarship/MotionalEMF.pdf

However, assuming Gene Mosca has not already posted a reference to
his paper (I only read the digests), you should look at his lovely
piece:

Magnetic Forces Doing Work? AJP 42:205 (1974)

Should be required reading for those teaching this topic. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/