Two large thin parallel metal plates have surface charge densities of equal magnitude but opposite signs $(\sigma = 26.4 \times 10^{-12} \ C/m^2)$. The electric field between these plates is ........ $N/C$.

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is . . . . . . . (All quantities are measured in $SI$ units).

$A$ thin metallic spherical shell of radius $r$ contains a charge $Q$ on its surface. $A$ point charge $q_1$ is placed at the centre of the shell and another charge $q_2$ is placed outside the shell at a distance $x$ from the centre. Then, the forces on charges $q_1$ and $q_2$ respectively are

$A$ 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 $\epsilon_{0} = 8.85 \times 10^{-12} \ C^{2} \ N^{-1} \ m^{-2}$]

$A$ uniformly charged thin spherical shell of radius '$R$' has a uniform surface charge density '$\sigma$'. It is made of two identical hemispherical shells held together by pressing them with a force '$F$' as shown. '$F$' is proportional to [$\epsilon_0$ = permittivity of free space].

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