Two long thin charged rods with charge density $\lambda$ each are placed parallel to each other at a distance $d$ apart. The force per unit length exerted on one rod by the other will be (where $k = \frac{1}{4 \pi \varepsilon_0}$)

The electric field intensity on the surface of a solid charged sphere of radius $r$ and volume charge density $\rho$ is ( $\epsilon_0=$ permittivity of free space).

Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is

As shown in the figure, a cuboid lies in a region with an electric field $\vec{E} = 2x^2 \hat{i} - 4y \hat{j} + 6 \hat{k} \; \text{N/C}$. The magnitude of the charge within the cuboid is $n \varepsilon_0 \; \text{C}$. The value of $n$ is $............$ (the dimensions of the cuboid are $1 \times 2 \times 3 \; \text{m}^3$ along the $x, y, z$ axes respectively).

For an infinite line of charge having charge density $\lambda$ lying along the $x$-axis,the work required in moving a charge $q$ from point $C$ to point $A$ along the arc $CA$ is:

$A$ charge $17.7 \times 10^{-4} \ C$ is distributed uniformly over a large sheet of area $200 \ m^2$. The electric field intensity at a distance $20 \ cm$ from it in air will be $\left[\varepsilon_0=8.85 \times 10^{-12} \ C^2/Nm^2\right]$