The charge distribution is shown in the figure below. The electric flux through the surface $S$ due to these charges is .........

$A$ point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $ABCD$?

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

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.

$(a)$ An electrostatic field line is a continuous curve. That is,a field line cannot have sudden breaks. Why not?
$(b)$ Explain why two field lines never cross each other at any point?

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss's theorem because