Consider a uniform electric field $\vec{E} = 3 \times 10^3 \hat{k} \text{ N C}^{-1}$. The electric flux of this field through a square of $20 \text{ cm}$ on a side whose plane is parallel to the $yz$-plane is $....... \text{ N m}^2 \text{ C}^{-1}$.

$A$ point charge $q$ is placed at the center $O$ of a cube of side length $L$. Another identical charge $q$ is placed at a distance $L$ from $O$ as shown in the figure. The electric flux through the face $ABCD$ is:

Two co-axial conducting cylinders of same length $\ell$ with radii $\sqrt{2} R$ and $2 R$ are kept,as shown in Fig. $1$. The charge on the inner cylinder is $Q$ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $\kappa=5$. Consider an imaginary plane of the same length $\ell$ at a distance $R$ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. $2$. Ignoring edge effects,the flux of the electric field through the plane is ($\epsilon_0$ is the permittivity of free space):

$A$ charge of $20 \ \mu C$ is placed inside a closed surface. If an additional charge of $80 \ \mu C$ is placed inside the surface,the change in flux is:

$A$ uniformly charged conducting sphere of diameter $14 \ cm$ has a surface charge density of $40 \ \mu C/m^2$. The total electric flux leaving the surface of the sphere is nearly (Permittivity of free space $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2/N \cdot m^2$)

$A$ charge $Q$ is placed at the center of a closed cube. The flux passing through any one face of the cube will be .......