It's a given that the rectangle is fixed to the ground..
So apart from the fact that the magnetic field in it changes direction all the time, B's size is constant
well usually in these kind of questions where there is some kind of change in the capacitor (the plates were move closer for instance)- We need to calculate the energy in the system before the change, calculate the energy afterwards and see the change's size and sign.
But in this problem I...
OK... As I try your idea I get into the following dilemma: which way is V? The movement of the rod or the movement of the current?
Unfortunately neither one of those options creates a force upwards using the right hand rule... \: