Induction

I don't know from where you got the picture that there is no induced emf when a metal plate is moving in a (consntant) magnetic field. This is not true. There is indeed an induced emf, similar to the situation that a metal rod is moving in a magnetic field.

As what you have learnt from your high school physics, the basic principle for an induced emf to occur is that there is "cutting of magnetic field lines" by the conductor when it moves in the field. Faraday expressed this phenomenon quantitatively as the "rate of change of magnetic flux", which was formulated as the Faraday's Law of Electromagentic Induction.

A metal plate can be regarded as a number of metallic strips joint together. Each of these strips behaves like a metallic rod. When these strips are made to cut magnetic field lines, emf will be induced. The polarity of induced emf can be found by applying Fleming's Right Hand Rule.

In fact, induced emf in metal disk is employed in producing eddy current in a lot of applications, such as electromagnetic braking.