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

The correct answer is 288.

E=E0​×i^
ϕnet ​=ϕABCD​=E0​a⋅a2
ϵ0​qen ​​=E0​a3
qen​=E0​∈0​a3
=4×104×9×10−12×8×10−6
=288×10−14C
Q=288