How can a moving rod in homogeneous magnetic field have changing enclosed flux?

Question

A conducting rod XY and a conducting rectangular loop ABCD are placed in infinitely wide area with homogeneous magnetic field (not changing with respect to time). They are moved perpendicularly to the magnetic field as shown below.

The induced emf in ABCD is zero because there is no changing enclosed flux. I cannot digest how the rod XY can have non zero induced emf. It is a bit counter intuitive as in my mental model both have no changing enclosed flux.

Answer 1

Rod $XY$ has a motional emf (10.2) , $BLv$, induced and let us assume (as the direction of the magnetic filed is not specified) that end $Y$ is at the higher potential relative to end $X$.

In the second example magnitude of the motional emf due to rods $AB$ and $DC$ is the same, $BLv$, and so the net emf induced in the loop is zero as ends $B$ and $C$ are at a higher potential than ends $A$ and $D$.