$A$ charge $q$ is placed inside a hollow cylinder. The electric flux associated with the curved surface $B$ is $\phi$. The flux associated with a plane surface (either $A$ or $C$) will be:

$A$ large charged plane having surface charge density $4.9 \times 10^{-6} \text{ C m}^{-2}$ lies in the $x-y$ plane. $A$ circular plane of radius $1 \text{ cm}$ is lying completely in the region where $x, y$ and $z$ coordinates are all positive. When the plane's normal makes an angle $60^{\circ}$ with the $z$-axis,the electric flux through the circular plane is (Given: $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$)

Select the correct statement$(s)$:
$(1)$ The density of electric field lines is independent of the magnitude of the electric field vector $E$ at a given point.
$(2)$ The density of electric field lines is proportional to the magnitude of the electric field vector $E$ at a given point.
$(3)$ Electric field lines do not exist in reality. They are only a graphical representation of the electric field.
$(4)$ Electric field lines exist in reality.

$A$ $6 \mu C$ charge is placed at the centre of a cube. What will be the electric flux through each face of the cube? (Take $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}$)

$A$ charge of $20 \ \mu C$ is placed inside a closed surface. If an additional charge of $80 \ \mu C$ is placed inside the surface,the change in flux is:

The electric flux from a cube of edge $l$ is $\phi$. If an edge of the cube is made $2l$ and the charge enclosed is halved,its value will be