An infinite line charge produces a field of $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. The linear charge density is . . . . . . . $\left(k = 9 \times 10^9 \text{ Nm}^2/\text{C}^2\right)$ (in $\text{ } \mu\text{C/m}$)

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

Three infinitely long charged sheets are placed as shown in the figure. The electric force acting on a charge $-q$ placed at the point $P$ is ($\sigma=$ surface charge density,$\varepsilon_0=$ permittivity of free space).

An electric dipole is placed on the $x$-axis in proximity to a line charge with a linear charge density of $3.0 \times 10^{-6} \, C/m$. The line charge is placed on the $z$-axis. The positive and negative charges of the dipole are at distances of $10 \, mm$ and $12 \, mm$ from the origin,respectively. If a total force of $4 \, N$ is exerted on the dipole,find the magnitude of the positive or negative charge of the dipole.

$A$ 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.

The electric field intensity at a point between two parallel sheets with like charges of the same surface charge density $(\sigma)$ is: