A point charge of $+\,12 \,\mu C$ is at a distance $6 \,cm$ vertically above the centre of a square of side $12\, cm$ as shown in figure. The magnitude of the electric flux through the square will be ....... $\times 10^{3} \,Nm ^{2} / C$

Gauss's law can help in easy calculation of electric field due to

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

In $1959$ Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be : 

${e_p}{\rm{ }} =  - {\rm{ }}\left( {1{\rm{ }} + {\rm{ }}y} \right)e$ where $\mathrm{e}$ is the electronic charge.

$(a)$ Find the critical value of $y$ such that expansion may start.

$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.

Let the electrostatic field $E$ at distance $r$ from a point charge $q$ not be an inverse square but instead an inverse cubic, e.g. $E =k \cdot \frac{q}{r^{3}} \hat{ r }$, here $k$ is a constant.

Consider the following two statements:

$(I)$ Flux through a spherical surface enclosing the charge is $\phi=q_{\text {enclosed }} / \varepsilon_{0}$.

$(II)$ A charge placed inside uniformly charged shell will experience a force.

Which of the above statements are valid?

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