A thin, nonconducting disk of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a uniform positive surface charge density \(\sigma\), giving a total charge \(Q = \sigma \pi R^2\).

The electric potential at a point on the positive \(z\)-axis is given by \(V(z) = \dfrac{\sigma}{2\varepsilon_0}\left(\sqrt{z^2 + R^2} - z\right)\).

Which of the following correctly describes the behavior of the potential \(V(z)\) and the axial electric field component \(E_z(z) = -\dfrac{dV}{dz}\) in the asymptotic limits \(z \ll R\) and \(z \gg R\)?