In a region of space, the electric field is in the x direction and is given as $\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\mathrm{x}.\hat{\mathrm{i}}$. Consider an imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates. The charge inside this volume is

 

Electric field is perpendicular to the shaded faces shown in figure along +ve x-axis.  $\overrightarrow{\mathrm{E}}$ is parallel to the remaining four faces and hence fluxes through them are zero.

At face (1), E = 0 as x = 0 and flux = 0

Net flux through the cube = flux through the face (2) = EA = (E₀a)a² = E₀a²

$\mathrm{\varphi }=\frac{{\mathrm{q}}_{\mathrm{in}}}{{\mathrm{\epsilon }}_0}\Rightarrow \mathrm{E}.{\mathrm{a}}^2=\frac{{\mathrm{q}}_{\mathrm{in}}}{{\mathrm{\epsilon }}_0}, \mathrm{here} \mathrm{E}={\mathrm{E}}_{\mathrm{o}}\mathrm{a}$

$\Rightarrow {\mathrm{q}}_{\mathrm{in}}={\mathrm{\epsilon }}_0{\mathrm{E}}_0{\mathrm{a}}^3$