Find out the surface charge density at the intersection of point $x =3\, m$ plane and $x$ -axis, in the region of uniform line charge of $8\, nC / m$ lying along the $z$ -axis in free space.

A metallic shell has a point charge ‘$q$’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces

The total charge enclosed in an incremental volume of $2 \times 10^{-9} \,{m}^{3}$ located at the origin is ...... $nC,$ if electric flux density of its field is found as $D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}$

Draw electric field lines of simple charge distribution.

Obtain Gauss’s law from the flux associated with a sphere of radius $\mathrm{'r'}$ and charge $\mathrm{'q'}$ at centre.

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