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  4. 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 vecE=E0 x hat t . Where E0=4 × 104 NC -1 m -1. If a=2 cm, the charge contained in the cubical volume is Q × 10-14 C. The value of Q is Take .E0=9 × 10-12 C 2 / Nm 2)

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Q. 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 $\left.E_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$

JEE MainJEE Main 2023Electric Charges and Fields

Solution:

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$ \vec{ E }= E _0 \times \hat{ i } $
$ \phi_{\text {net }}=\phi_{ ABCD }= E _0 a \cdot a ^2$
$ \frac{ q _{\text {en }}}{\epsilon_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$