Why is there an emf induced across the width of a metal sheet when it is moved across a uniform magnetic field? By Faraday's law, the flux is constant, so there will be no emf. But each electron in the metal sheet is moved at some speed, so it will experience a force, and as a result, electrons will accumulate at the edges of the metal sheet ( basically, the hall effect ). I've asked a similar question before, and it involved me incorrectly applying Faraday's law; is that also the case here? 
 A: As dmckee points out in the comments, Faraday's law essentially states that the line integral of the electric field along a closed path is proportional to the rate of change of magnetic flux through a surface bounded by the closed path.  This line integral gives the emf associated with the loop.
Since the flux through a surface bounded by the path you've drawn has constant magnetic flux through (by stipulation), the emf as defined above, is zero.
If you were to connect a conductor to the edges of the plates along the path you've drawn, there would be no (steady) current since there is no emf.
The reason is that the Lorentz force on the electrons in the attached conductor are driven in the opposite sense around the loop as the electrons in the plate.
In this scenario, to get an emf and thus drive charge along a closed conductive path, you must arrange things such that the magnetic flux threading the conductive path changes with time.
One way to do this is let the plate rest on conductive rails that are connected to a load at their ends like so:  

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