$A$ cube of side $l$ is placed in a uniform electric field $E$,where $E = E\hat{i}$. The net electric flux through the cube is:

If electric flux through a cubic Gaussian surface is $1.9 \times 10^5 \text{ Nm}^2 \text{C}^{-1}$,then the electric charge at its center is . . . . . . . (Edge length of cube = $9.0 \text{ cm}$).

$A$ square loop of sides $a=1 \ m$ is held normally in front of a point charge $q=1 \ C$. The charge is placed at a distance of $a/2$ from the center of the square. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{\varepsilon_0} \frac{N m^2}{C}$,where the value of $p$ is . . . . . . .

Why do two electric field lines not intersect each other?

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):

$q_1, q_2, q_3$ and $q_4$ are point charges located as shown in the figure,and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?