Figure shows a rectangular conductor PQRS in which the conductor PQ is free to move. The conductor PQ is moved towards the left with a constant velocity V as shown in the figure. Assume that there is no loss of energy due to friction. What will be the magnetic flux linked with the loop PQRS and the motional emf?

Magnetic flux = $Blx$; Motional emf = $BIV$

The correct answer is Option (3) → Magnetic flux = $Blx$; Motional emf = $BIV$

Magnetic flux linked with loop PQRS:

The flux through the loop = magnetic field × area (field is uniform and perpendicular to plane).

Area = length of side PR (call it $l$) × horizontal separation $x$ (between PQ and the opposite side).

$\Phi = B\,l\,x$

Motional emf induced in the moving rod PQ:

For a rod of length $l$ moving with velocity $V$ perpendicular to a magnetic field $B$, the motional emf is

$\mathcal{E} = B\,l\,V$

Therefore:

Magnetic flux = $B l x$; Motional emf = $B l V$