A thin, nonconducting ring of radius \(R\) lies in the \(xy\)-plane centered at the origin and carries a positive charge \(Q\) distributed uniformly along its circumference. The electric potential at a point on the positive \(z\)-axis is given by \(V(z) = \dfrac{Q}{4\pi\varepsilon_0\sqrt{z^2 + R^2}}\). Using the relationship between electric potential and electric field, which of the following gives the electric field vector \(\vec{E}(z)\) on the positive \(z\)-axis and its correct first-order approximation in the limit \(z \gg R\)?