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)

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

$A$ charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$. If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is. . . . . . .

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

$A$ field line is shown in the figure. This field line cannot represent:

$A$ hemispherical surface of radius $a$ is placed in a uniform electric field $E$ such that the flat surface makes an angle of $\pi /4$ with the vertical. There is no charge inside the hemisphere. The electric flux passing through the curved surface of the hemisphere is: