A charge $Q$ is fixed at a distance $d$ in front of an infinite metal plate. The lines of force are represented by

Units of electric flux are 

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi _1}$ and ${\varphi _2}$ the electric charge inside the surface will be

Gauss’s law should be invalid if

The electric field components in Figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \;N / C\, m ^{1 / 2} .$ Calculate

$(a)$ the flux through the cube, and

$(b)$ the charge within the cube. Assume that $a=0.1 \;m$

The total charge enclosed in an incremental volume of $2 \times 10^{-9} \,{m}^{3}$ located at the origin is ...... $nC,$ if electric flux density of its field is found as $D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}$