The figure shows the electric field lines of three charges with charges $+1, +1$,and $-1$. The Gaussian surface in the figure is a sphere containing two of the charges. The total electric flux through the spherical Gaussian surface is

$A$ positive charge $q$ is placed at the centre of a neutral hollow cylindrical conducting shell with its cross-section as shown in the figure below. Which one of the following figures correctly indicates the induced charge distribution on the conductor? (Ignore edge effects)

In a region, the intensity of an electric field is given by $E = 2i + 3j + k$ in $NC^{-1}$. The electric flux through a surface $S = 10i \ m^2$ in the region is

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}$ (where $\varepsilon_0$ is the permittivity of free space),then the value of $n$ is

$A$ point charge $+Q$ is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is:

Why do two electric field lines not intersect each other?