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

A cube of a metal is given a positive charge $Q$. For the above system, which of the following statements is true

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.

A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_0}$ (in SI units). The value of $n$ is. . . . 

A charged body has an electric flux $\phi$ associated with it. The body is now placed inside a metallic container. The flux $\phi$, outside the container will be

If the number of electric lines of force emerging out of a closed surface is $1000$ , then the charge enclosed by the surface is .......... $C$