Physics Question from JEE Main 2023 · 1 February, Shift 2

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 $\vec{E} = E_0 x \hat{i}$. Where $E_0 = 4 \times 10^4 \; \text{N C}^{-1} \text{m}^{-1}$. If $a = 2 \, \text{cm}$, the charge contained in the cubical volume is $Q \times 10^{-14} \, \text{C}$. The value of $Q$ is _____. (Take $\epsilon_0 = 9 \times 10^{-12} \, \text{C}^{2}/\text{N m}^{2}$)