A uniformly charged thin rod lies along the \(x\) axis from \(x=0\) to \(x=+\infty\).

(a) Derive an expression for the component \(E_{y}\) of the electric field in the positive \(y\) direction, and

(b) show that the electric field at all positions on this axis makes an angle of \(135^{\circ}\) with the rod.