$A$ charge $q$ is placed at the center of one of the faces of a cube. What is the electric flux linked with the cube?

$A$ charge $q$ is placed at one corner of a cube as shown in the figure. The flux of the electrostatic field $\overrightarrow{E}$ through the shaded area is ...... .

$A$ point charge '$Q$' is placed at a point inside a hollow conducting sphere. Which of the following electric field patterns is correct?

$A$ sphere encloses an electric dipole with charges $\pm 3 \times 10^{-6} \; C$. What is the total electric flux across the sphere in $\text{N m}^2 / \text{C}$?

The total electric flux through a closed spherical surface of radius $r$ enclosing an electric dipole of dipole moment $2aq$ is (Give $\varepsilon_0=$ permittivity of free space)

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.