A rigid planar rectangular wire loop of width \(w\) and length \(\ell\) lies in the \(xy\)-plane with its sides parallel to the coordinate axes. A time-independent, spatially non-uniform magnetic field perpendicular to the loop is described by \(\vec{B}(x, y, z) = \beta x\,\hat{k}\), where \(\beta\) is a positive constant. The loop moves in the \(+y\)-direction with a constant velocity \(\vec{v} = v_0\,\hat{j}\).

Which of the following statements correctly describes the net induced electromotive force (EMF) around the loop and provides the correct physical justification?