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

If the atmospheric electric field is approximately $150 \,V/m$ and the radius of the Earth is $6400 \,km$,then the total charge on the Earth's surface is .......... coulomb.

The electric field $\vec{E} = E_0 y \hat{j}$ acts in a space where a cylinder of radius $r$ and length $l$ is placed with its axis parallel to the $y$-axis. The charge inside the volume of the cylinder is:

$A$ 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. Find the final charge distribution on the surfaces.

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 \,m$ from $S$ and has a speed of $1 \,m/s$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1 \,s$ is $\alpha \left[ \frac{m \epsilon_0}{e} \right] \,C/m^2$. The value of $\alpha$ is:

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