Two surfaces $S_1$ and $S_2$ are shown in figure. Flux associated with $S_1$ is ${\phi _1}$ and $S_2$ is ${\phi _2}$. Which is correct ?

What will be the total flux through the faces of the cube as in figure with side of length $'a'$ if a charge $'q'$ is placed at ?

$(a)$ $C$ $:$ centre of a face of the cube.

$(b)$ $D$ $:$ midpoint of $B$ and $C$.

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 rectangular surface of sides $10 \,cm$ and $15 \,cm$ is placed inside acyniform electric field of $25 \,V / m$, such that the surface makes an angle of $30^{\circ}$ with the direction of electric field. Find the flux of the electric field through the rectangular surface .................. $Nm ^2 / C$

Consider an electric field $\vec{E}=E_0 \hat{x}$, where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is

What can be said for electric charge if electric flux assocaited with closed loop is zero ?