A doubt on electromagnetic induction?
First of all I have to apologize that English is not my native language so I'm not sure if "E.M.F." is that what I think it is.

However if my understanding is right then this is the voltage induced between the ends of the wires. I named this voltage "Ui" in the following drawing:



If my understanding is correct and the magetic field is uniform then this voltage is proportional to the "triple product" of the of the vector of the motion of the wire (v), the vector describing the magnetic field (B) and the vector between the two ends of the wires (direct line - named "x" in the drawing).

The "triple product" can be seen as the volume of the body formed by v, x and B (right side of the picture).

In this case the magnetic fields are the same and the motion of the wires are also the same. B, v and x are ortogonal to one another so Ui is proportional to the product B*v*x.

The length of x is maximal in case 4 so the EMF is also maximal in this case.

And how about the magnetic flux?

If you want to measure this voltage you'll have to take some instrument (like a multimeter) which has wires itself.

If the EMF induced in the wire would be Ui then the EMF in the wires of the measurement instrument would be (-Ui) (the ends of the wires are in the same position) so you have two voltage sources in series and the resulting voltage measured by your instrument would be U=Ui-Ui=0.

You might also argue that the wires of the measurement instrument and the wire to be measured form one long wire and the starting and the end point of this large wire is the same (the location of the measurement instrument) so the length "x" is zero.

This is not the case if the wires belonging to the measurement instrument are outside of the magetic field or the wires of the measurement instrument are not moving themselves.

In this case however the magenetic flux will definitely change when the wire is moving. You can prove that the derivation d/dt of the magentic flux is proportional to B*v*x in this case...