incrediblyfrustrated said:
Hi, I'm trying to understand how a moving conductor traveling with a constant velocity in a uniform magnetic field can produce an emf of -Blv...
I believe that this is where you ran into a problem. There is a slight mistake in the terminology you used in describing your scenario. That caused a bit of a problem in correctly stating your question.
You see, the term "emf" means
electromotive force which is defined as follows:
https://en.wikipedia.org/wiki/Electromotive_force
Electromotive force, also called
emf (denoted
and measured in volts) is the voltage developed by any source of electrical energy such as a battery or dynamo. It is generally defined as the electrical potential for a source in a circuit. A device that supplies electrical energy is called a seat of electromotive force or
emf. Emfs convert chemical, mechanical, and other forms of energy into electrical energy. The product of such a device is also know as
emf.
While this is the term you used the concept you described was more along the lines of a motional EMF. You see, a motional EMF is a closed line integral around a closed circuit. In your diagram there is no closed circuit. However there will be a difference in potential between the two ends and this kind of difference in potential you can measure with a volt meter.
Note: You might wonder what kind of difference in potential you can't measure with a volt meter. Consider a spherically charged object at
r = (0, 0, 0). There will be an electric field around this object and there will be a difference in potential between two points at different radii. If you placed a voltmeter between two such points it will read zero. There's a subtle difference between these two scenarios which you have to be careful about. Here's why: in the example you gave there will be no flow of current in the wire, all that exists is a difference in potential across the conductors ends and that's it. If instead you placed a conductor shaped like a square loop whose sides are parallel to the xy-axes in a magnetic field in the -z-direction where the loop is moving in the +x direction (or any direction which keeps it in the xy-plane) then there will still be no current in the conductor. However if the field exists only in the +x side of the y-axes and the loop is in motion such that the magnetic field is only in part of the loop then the flux will be changing and there will be a non-zero emf in the wire and there will now be a current.
If you worked this out using the closed integral that defines the emf in he circuit then this will make a lot more sense. I wish I could easily draw and attach a diagram.