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.

Electric field in a region is uniform and is given by $\vec{E}=a \hat{i}+b \hat{j}+c \hat{k}$. Electric flux associated with a surface of area $\vec{A}=\pi R^2 \hat{i}$ is

A charged particle $q$ is placed at the centre $O$ of cube of length $L$ $(A\,B\,C\,D\,E\,F\,G\,H)$. Another same charge $q$ is placed at a distance $L$ from $O$.Then the electric flux through $BGFC$ is

The figure shows two situations in which a Gaussian cube sits in an electric field. The arrows and values indicate the directions and magnitudes (in $N-m^2/C$) of the electric fields. What is the net charge (in the two situations) inside the cube?

Eight dipoles of charges of magnitude $e$ are placed inside a cube. The total electric flux coming out of the cube will be

An electrostatic field line leaves at an angle $\alpha$ from point charge $q_{1}$ and connects with point charge $-q_{2}$ at an angle $\beta\left(q_{1}\right.$ and $q_{2}$ are positive) see figure below. If $q_{2}=\frac{3}{2} q_{1}$ and $\alpha=30^{\circ}$, then