A thin, nonconducting circular disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a uniform positive surface charge density \(\sigma\), corresponding to a total charge \(Q = \sigma \pi R^2\). The magnitude of the electric field at a point on the positive \(z\)-axis is given by the expression
\[E(z) = \dfrac{\sigma}{2\varepsilon_0} \left(1 - \dfrac{z}{\sqrt{z^2 + R^2}}\right)\]
Which of the following statements correctly describes the behavior of the electric field in the limits \(z \ll R\) and \(z \gg R\)?