Consider the four surfaces $S_1, S_2, S_3,$ and $S_4$ enclosing the same charge $q_1$ as shown in the figure. Compare the electric flux through these surfaces.

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.

Three charges $q_1 = 1\,\mu C, q_2 = 2\,\mu C$,and $q_3 = -3\,\mu C$ and four surfaces $S_1, S_2, S_3$,and $S_4$ are shown in the figure. The electric flux emerging through surface $S_2$ in $N\cdot m^2/C$ is:

$A$ charge $Q$ is enclosed by a Gaussian surface of radius $R$. If the radius is doubled,then the outward electric flux will

In a uniform electric field,a cube of side $1 \ cm$ is placed. The total energy stored in the cube is $8.85 \ \mu J$. The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is

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