$A$ charge $q$ is placed at the centre of the base of a cubical box of side $a$ with the top open. The flux of the electric field through the open surface is not considered,but the flux through the remaining five surfaces of the cubical box is:

$A$ metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

Choose the incorrect statement.

If the radius of the spherical Gaussian surface is increased,then the electric flux due to a point charge enclosed by the surface:

$A$ charged shell of radius $R$ carries a total charge $Q$. Let $\Phi$ be the flux of the electric field through a closed cylindrical surface of height $h$,radius $r$,with its center coinciding with that of the shell. The center of the cylinder is a point on the axis of the cylinder equidistant from its top and bottom surfaces. Which of the following option$(s)$ is/are correct? [$\epsilon_0$ is the permittivity of free space]
$(1)$ If $h > 2R$ and $r > R$,then $\Phi = \frac{Q}{\epsilon_0}$
$(2)$ If $h < \frac{8R}{5}$ and $r = \frac{3R}{5}$,then $\Phi = 0$
$(3)$ If $h > 2R$ and $r = \frac{4R}{5}$,then $\Phi = \frac{2Q}{5\epsilon_0}$
$(4)$ If $h > 2R$ and $r = \frac{3R}{5}$,then $\Phi = \frac{Q}{5\epsilon_0}$

$A$ hollow cylinder has a charge $q$ at its center. If $\phi$ is the electric flux associated with the curved surface $B,$ the flux linked with the plane surface $A$ will be $:-$