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1. Electric Charges and Fields
medium
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 $\overrightarrow{ E }= E _0 \times \hat{ i }$. 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 $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$
A
$280$
B
$250$
C
$260$
D
$288$
(JEE MAIN-2023)
Solution
$\overrightarrow{ E }= E _0 \times \hat{ i }$
$\phi_{\text {net }}=\phi_{ ABCD }= E _0 a a ^2$
$\frac{ q _{ en }}{\epsilon_0}= E _0 a ^3$
$q _{ en }= E _0 \in_0 a ^3$
$=4 \times 10^4 \times 9 \times 10^{-12} \times 8 \times 10^{-6}$
$=288 \times 10^{-14}\,C$
$Q =288$
Standard 12
Physics
