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

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

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 ?

$(a)$ $A$ $:$ a corner of the cube.

$(b)$ $B$ $:$ midpoint of an edge of the cube.

The figure shows the electric field lines of three charges with charge $+1, +1$, and $-1$. The Gaussian surface in the figure is a sphere containing two of the charges. The total electric flux through the spherical Gaussian surface is

If $\oint_s \vec{E} \cdot \overrightarrow{d S}=0$ over a surface, then:

A square surface of side $L$ meter in the plane of the paper is placed in a uniform electric field $E(volt/m)$ acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figure.The electric flux linked to the surface, in units of $volt \;m $