A charge Q is situated at a distance a/2 above the centre of a...

Consider a hypothetical cube of edge length $a$ such that the given square surface forms one of its six faces.

The charge $Q$ is placed at a distance $a/2$ above the center of the square surface, which corresponds exactly to the center of the hypothetical cube.

According to Gauss's law, the total electric flux passing through the closed surface of the cube is given by:

$\Phi_{\text{total}} = \dfrac{Q}{\varepsilon_0}$

Since the charge $Q$ is located symmetrically at the center of the cube, the electric flux is distributed equally among all six identical faces of the cube.

Therefore, the electric flux passing through the given square surface is:

$\Phi = \dfrac{1}{6} \Phi_{\text{total}} = \dfrac{Q}{6\varepsilon_0}$