$A$ $6 \mu C$ charge is placed at the centre of a cube. What will be the electric flux through each face of the cube? (Take $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ Nm^2 C^{-2}$)

The number of electric lines that emerge from a finite charge $+q$ is . . . . . . .

Total electric flux coming out of a unit positive charge placed in air is

Consider a cube of side length '$a$' centered at the origin. It is enclosed by three fixed point charges: $(-q)$ at $(0, -a/4, 0)$,$(+3q)$ at $(0, 0, 0)$,and $(-q)$ at $(0, a/4, 0)$. Choose the correct option.

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