Question

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 $\vec{E}=E_0 x \hat{ t }$ 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 \(E_{0}=9\times 10^{-2}C^{2}/Nm^{2}\)

Answer 1

Correct Answer: 288

The correct answer is 288.

$\vec{E}=E_0\times \hat{i}$
${\varphi }_{\text{net}}={\varphi }_{ABCD}=E_{0}a\cdot a^2$
$\frac{q_{\text{en}}}{{ϵ}_0}=E_0{a}^3$
$q_{en}=E_0{\in }_0{a}^3$
$=4\times 10^4\times 9\times 10^{-12}\times 8\times 10^{-6}$
$=288\times 10^{-14}C$
$Q=288$