Re: indiced emf ....

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

         On June 1997 Eugene P. Mosca" <mosca@nadn.navy.mil> wrote:

> If an electromagnetic field is observed from two distinct reference
> frames, the E and B fields get mixed up in the transformation from one
> frame to the other. [Gene was responding to Nick's example of a metallic
> rod moved rapidly in a uniform magnetic field.]  For Nick's example, in 
> the frame in which the rod is moving the static B field transforms to a 
> static B field and a static E field in the frame moving with the rod. 

> The observer on the rod considers this E field as the cause of the charge 
> separation in the rod. However, she observes no potential difference across 
> the rod because the rod is in electrostatic equilibrium in her reference 
> frame, so in this frame the electric field E induces charges on the surface 
> of the rod that result in the net electric field inside the material of the 
> conductor to be everywhere zero. Thus the rod is an equipotential. 

I agree with Nick that the situation can be turned into a paradox. One 
person, "she", observes no emf accross the rod while the other, "he", does 
observe it. He (the observer for whom v is not zero) strongly believes 
that + and - charges are separated. He concludes that the VOLUME DENSITY
of free electrons is excessive at one end and deficient at the other. But 
she (the observer sitting on the rod) does not detect any emf. Thus she
concludes that the volume densities of free electrons are identical at
two ends. Note that the speed of the wire, v, does not have to be of the 
same order as c.

On the other hand, according to Gene, she will observe SURFACE CHARGES
which are not observed by him. Who is right, he or she? How can they both 
be right? Why should a conclusion (about what happens to free electrons)
depend the frame of reference? "He" says that F=q*v*B is resposible for 
the separation of + and - while "she" is forced to say that surface charges 
appear to make sure that the electric field is zero everywhere inside
the moved rod. The "to make sure" term is troublesome; that is a good
subject for another thread.

........................ Another observation ............................

As pointed out by John M, "she" has no difficulties reading her local
voltmeter while the readings of "his" local voltmeter must be corrected 
to account for the Faraday effect in the leads or "rails". The correction 
is necessary even when a gold-leaf electrometer is used to measue the emf.
(for example, between the rails which support the ends of the moving wire)
Keep in mind, however, that many complications (of that correction) are 
eliminated when v<<c. And remember that, at least in principle, the emf 
differences can be demonstated without using additional leads. Think about 
the "corona" discharge from the needle-sharp ends on the moving wire; the 
air pressure can be reduced to enhance it. 

It does not make any sense to expect that "he" may see the corona which is 
not seen by "her". Do we have a real paradox here? 
                                                     Ludwik Kowalski