The number of lines of force originating from a point charge of $2 \times 8.85 \times 10^{-9} \text{ C}$ in a medium of dielectric constant $10$ is $(\epsilon_0 = 8.85 \times 10^{-12} \text{ SI unit})$.

$A$ uniform electric field $E = 3 \times 10^5 \text{ NC}^{-1}$ is acting along the positive $Y$-axis. The electric flux through a rectangle of area $10 \text{ cm} \times 30 \text{ cm}$ whose plane is parallel to the $ZX$-plane is

If charge $q$ is placed on one of the vertex of a cube, then total electric flux passing through the cube is . . . . . . .

$A$ point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential

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

$A$ circular disc of radius $R$ carries surface charge density $\sigma(r) = \sigma_0 \left(1 - \frac{r}{R}\right)$,where $\sigma_0$ is a constant and $r$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is $\phi_0$. Electric flux through another spherical surface of radius $\frac{R}{4}$ and concentric with the disc is $\phi$. Then the ratio $\frac{\phi_0}{\phi}$ is: