(N/A) The electric flux $\phi$ associated with an area vector $\overrightarrow{S}$ in an electric field $\overrightarrow{E}$ is given by the dot product:
$\phi = \overrightarrow{E} \cdot \overrightarrow{S} = ES \cos \theta$,where $\theta$ is the angle between the electric field vector $\overrightarrow{E}$ and the area vector $\overrightarrow{S}$.
$(i)$ If $\theta = 90^{\circ}$,then $\cos 90^{\circ} = 0$,so $\phi = 0$. This occurs when the electric field lines are parallel to the surface (i.e.,the area vector is perpendicular to the field).
(ii) If $\theta < 90^{\circ}$,then $\cos \theta > 0$,so $\phi > 0$. This occurs when the electric field lines are directed outward from the closed surface.
(iii) If $\theta > 90^{\circ}$,then $\cos \theta < 0$,so $\phi < 0$. This occurs when the electric field lines are directed inward into the closed surface.