$A$ charge $Q$ is placed at the centre of a cube of side $a$. The total flux of electric field through the six surfaces of the cube is

Consider four closed surfaces $S_1, S_2, S_3,$ and $S_4$ each enclosing the same charge $q_1$. Compare the electric flux through these surfaces.

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):

$A$ positive charge $q$ is kept at the center of a thick shell of inner radius $R_1$ and outer radius $R_2$ which is made up of conducting material. If $\phi_1$ is the flux through a closed Gaussian surface $S_1$ whose radius is just less than $R_1$ and $\phi_2$ is the flux through a closed Gaussian surface $S_2$ whose radius is just greater than $R_1$,then:

The linear charge density of a wire is $8.85\,\mu C/m$. The radius and height of the cylinder are $3\,m$ and $4\,m$ respectively. Find the electric flux passing through the cylinder.

Why do two electric field lines not intersect each other?