Does emf get induced for any conductor moving perpendicularly to a magnetic field?
In the textbook explanation, they gave an example of a fixed metal frame over which a metal rod can roll. The field goes into the area of the frame and the rod moves horizontally over the frame, such that its motion is perpendicular to the field. In this case, the area bounded by the frame and the rod keeps changing, hence the flux changes, and an emf is induced.
But consider a case where there is no frame, and the rod is just moving perpendicular to a magnetic field with constant velocity. Is emf still induced across the ends of the rod?
Also, is the shape of the conductor of any significance? For example, replace the straight rod with a semicircular one in the above question.