The electric field in a region is given $\vec E = a\hat i + b\hat j$ . Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to $y-z$ plane

A point charge causes an electric flux of $-1.0 \times 10^{3}\; N\;m ^{2} / C$ to pass through a spherical Gaussian surface of $10.0\; cm$ radius centred on the charge.

$(a)$ If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

$(b)$ What is the value of the point charge?

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 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

A hollow cylinder has a charge $q$ coulomb within it. If $\phi$ is the electric flux in units of $volt-meter$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be

If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be