An infinite line charge produces a field of $7.182 \times 10^8 \, N/C$ at a distance of $2 \, cm$. The linear charge density is

Consider a long uniformly charged cylinder having constant volume charge density $\rho$ and radius $R$. $A$ Gaussian surface is in the form of a cylinder of radius $r$ such that the vertical axis of both cylinders coincide. For a point inside the cylinder $(r < R)$,the electric field is directly proportional to

$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$,where $\rho_0$ is a constant and $r$ is measured from the centre. Consider two points $A$ and $B$ at distances $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

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 $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$):

$A$ negatively charged plate has a surface charge density of $\sigma = 2 \times 10^{-6} \ C/m^2$. An electron with kinetic energy $KE = 200 \ eV$ is projected towards the plate. If the electron does not strike the plate,find the minimum initial distance $r$ in $mm$ from the plate.