A closed right circular cylinder of radius \(R\) and length \(L\) (where \(L > 2R\)) is centered at the origin with its central axis aligned along the \(z\)-axis. An infinitely long, thin wire carrying a uniform linear charge density \(\lambda\) is oriented parallel to the \(x\)-axis and lies in the \(xy\)-plane at a distance \(d\) (where \(0 < d < R\)) from the origin, passing through the cylinder. Which of the following expressions represents the net electric flux \(\Phi_E\) through the entire closed surface of the cylinder?