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A cubical volume is bounded by the surfaces $\mathrm{x=0, x=\mathrm{a}, y=0, y=\mathrm{a}, z=0, z=\mathrm{a}}$ . The electric field in the region is given by $\mathrm{\overrightarrow{\mathrm{E}}=\mathrm{E}_0 x \hat{\imath}}$ . Where $\mathrm{\mathrm{E}_0=4 \times 10^4 \mathrm{NC}^{-1} \mathrm{~m}^{-1}}$ . If $\mathrm{\mathrm{a}=2 \mathrm{~cm}}$ , the charge contained in the cubical volume is $\mathrm{Q \times 10^{-14} \mathrm{C}}$ . The value of $\mathrm{Q }$ is__________________.(Take $\mathrm{\in_{0}=9\times 10^{-12}C^{2}/Nm^{2}}$ )
Option: 1
288

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{\begin{aligned} & \phi=\mathrm{\overrightarrow{E}} \cdot \mathrm{\overrightarrow{A}} \\ & \mathrm{E}=\mathrm{E}_0 \mathrm{ai} \end{aligned}}$

$\mathrm{ \phi=\mathrm{E}_0 \mathrm{a} \cdot \mathrm{a}^2=\mathrm{E}_0 \mathrm{a}^3 }$
$\mathrm{\mathrm{q}_{\text {enc. }} =\phi \varepsilon_0 }$
$\mathrm{\mathrm{q}_{\text {enc. }} =\mathrm{E}_0 \mathrm{a}^3 \varepsilon_0 }$
$\mathrm{ =4 \times 10^4 \times 8 \times 10^{-6} \times 9 \times 10^{-12} }$
$\mathrm{\mathrm{q}_{\text {enc. }} =288 \times 10^{-14} \mathrm{C}}$
Hence the value of $\mathrm{\mathrm{Q} \: is \: 288 .}$

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