The magnetic flux density is constant, and the rod is being moved inside the field.
And if an emf is induced, how does the flux linkage change in this rod? The cross sectional area of this rod remains constant, so there shouldn't be a change in flux linkage. I feel like I'm getting something wrong here, but I just can't understand it.
Also, I would appreciate if the answers could be given in language a 12th grader can understand, I've looked at some of the other answers on here and I can't understand the maths of it all. I'm clear on integration, but we haven't done vector fields or even vector calculus yet, so I'd appreciate if those could be kept out (or simplified)