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=E₀ x i. 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 ε₀=9 × 10⁻¹² ~C² / Nm²)

Electrostatics: JEE Main 2023 Physics question

JEE Main 2023 · 1 Feb, Evening shift · Q61

JEE Main 20231 Feb, Evening shiftPhysicsHardElectrostatics167× since 2002

A cubical volume is bounded by the surfaces

\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}

. The electric field in the region is given by

\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}

. Where

\mathrm{E}_{0}=4 \times 10^{4} ~\mathrm{NC}^{-1} \mathrm{~m}^{-1}

. If

\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

\epsilon_{0}=9 \times 10^{-12} ~\mathrm{C}^{2} / \mathrm{Nm}^{2}

)

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