If the electric field is given by $(5 \hat{i}+4 \hat{j}+9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units)

A square surface of side $L$ metres is in the plane of the paper. A uniform electric field $\vec E(V/m) $, also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is

When the electric flux associated with closed surface becomes positive, zero or negative ?

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.

Gauss’s law states that

The electric flux passing through the cube for the given arrangement of charges placed at the corners of the cube (as shown in the figure) is