The electric field in a region of space is given by, $\overrightarrow E  = {E_0}\hat i + 2{E_0}\hat j$ where $E_0\, = 100\, N/C$. The flux of the field through a circular surface of radius $0.02\, m$ parallel to the $Y-Z$ plane is nearly

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?

A point charge $+10\; \mu \,C$ is a distance $5 cm$ directly above the centre of a square of side $10 \;cm ,$ as shown in Figure. What is the magnitude of the electric flux through the square?

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface $S$ is

A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$ If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ 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