A cubical volume is bounded by the surfaces $x =0, x = a , y =0, y = a , z =0, z = a$. The electric field in the region is given by $\overrightarrow{ E }= E _0 \times \hat{ i }$. Where $E _0=4 \times 10^4 NC ^{-1} m ^{-1}$. If $a =2 cm$, the charge contained in the cubical volume is $Q \times 10^{-14} C$. The value of $Q$ is $...........$

Take $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$ 

An infinite, uniformly charged sheet with surface charge density $\sigma$ cuts through a spherical Gaussian surface of radius $R$ at a distance $x$ from its center, as shown in the figure. The electric flux $\Phi $ through the Gaussian surface is

The $S.I.$ unit of electric flux is

Two infinite plane parallel sheets separated by a distance $d$ have equal and opposite uniform charge densities $\sigma $. Electric field at a point between the sheets is

Consider a uniform electric field $E =3 \times 10^{3} i\; N / C .$

$(a)$ What is the flux of this field through a square of $10 \;cm$ on a side whose plane is parallel to the $y z$ plane?

$(b)$ What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the $x -$axis?

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 ....... $\times 10^{3} \,Nm ^{2} / C$