An infinite line charge produces a field of $9 \times 10^4 \ NC^{-1}$ at a distance of $2 \ cm$. Its linear charge density is

$A$ large metal plate has a surface charge density of $8.85 \times 10^{-6} \ C \ m^{-2}$. An electron having initial kinetic energy of $8 \times 10^{-17} \ J$ is moving towards the center of the plate. If the electron stops just before reaching the plate,then the initial distance between the electron and the plate is [Take $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]

In the figure,a very large plane sheet of positive charge is shown. $P_{1}$ and $P_{2}$ are two points at distances $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density,then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P_{1}$ and $P_{2}$ respectively are:

An infinite non-conducting sheet has a surface charge density $2 \times 10^{-7} \text{ C/m}^2$ on one side. The distance between two equipotential surfaces whose potential difference is $90 \text{ V}$ is (assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$):

What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Charge $-q$ is distributed on the surfaces as: