A thin circular ring of radius \(R\) lies in the \(xy\)-plane, centered at the origin. The ring carries a non-uniform linear charge density given by \(\lambda(\theta) = \lambda_0 \cos\theta\), where \(\lambda_0\) is a positive constant and \(\theta\) is the polar angle measured counterclockwise from the positive \(x\)-axis. A point \(P\) is located on the positive \(z\)-axis at a distance \(z\) from the origin. Which of the following expressions gives the magnitude of the net electric field at point \(P\)?