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 E = E 0 × i. Where E 0=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. 0=9 × 10-12 C 2 / Nm 2)

JEE Mains · Physics · STD 12 - Electric charges and fields

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 \(\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)\)

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Verified Solution

Correct Answer

(D) \(288\)

Detailed explanation

\(\overrightarrow{ E }= E _0 \times \hat{ i }\)

\(\phi_{\text {net }}=\phi_{ ABCD }= E _0 a a ^2\)

\(\frac{ q _{ en }}{\epsilon_0}= E _0 a ^3\)

\(q _{ en }= E _0 \in_0 a ^3\)

\(=4 \times 10^4 \times 9 \times 10^{-12} \times 8 \times 10^{-6}\)

\(=288 \times 10^{-14}\,C\)

\(Q =288\)

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