A metal rod moving thru a magnetic field

[Nikitin]

Hi. A metal rod is moving thru a homogeneous magnetic field, standing 90 degrees upon it and the movement direction.

Supposedly there is a voltage between the two ends of the rod due to the moving. But why? The magnetic flux doesn't change!

I know that the voltage is supposed to be W/Q = vBq*L/q where L is the length of the rod, but still isn't faraday's law of induction (generated voltage = flux change) broken?

See the uploaded picture for further info

 

[Nikitin]

Check the picture inside the attached word-file.

A rod lies frictionless on two rails. When the circuit is opened the rod starts moving to the right by itself. What is the direction of the current inside the circuit?

I say it's against the clock, and the magnetic field tries to counteract it and change the direction of the current. The book says it's with the clock, and the magnetic field tries to counteract it.

Why am I wrong?

Additionally, the book claims that rod will eventually get a constant speed to the right. Why? That means the magnetic flux is constantly increasing, and according to Lenz's rule the rod should eventually STOP, not keep going!

 

[Nikitin]

Help? I've got exams on Tuesday, I really need help