A horizontal rectangular sheet of length \(\ell\) and width \(w\) is positioned with its center a vertical distance \(w / 2\) below an infinitely long positively charged rod that has a uniform linear charge density \(\lambda\).

(a) If the sides of length \(\ell\) are parallel to the rod's axis, what is the magnitude of the electric flux through the sheet?

(b) If the vertical distance between the sheet center and the rod is reduced to \(w / 4\), does the flux magnitude increase, decrease, or stay the same?