A cubical volume is bounded by the surface x=0, x=a, y=0, y=a, z=0, z=a. The electric field in the region is given by E→=E0xi^. Where E0=4×104NC−1m−1. If a=2 cm, the charge contained in the cubical volume is Q×10−14C. The value of Q is _____.(Take ϵ0=9×10−12C2/Nm2).

Given, E¯=E0xi^ and E0=4×104Nc−1m−1a=2×10−2mElectric flux, ϕE=E¯⋅A¯⇒qε0=EA⇒q=ε0EAq=9×10−12×4×104×2×10−2×4×10−4q=288×10−14 C∴Q=288

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A cubical volume is bounded by the surface $x = 0, x = a, y = 0, y = a, z = 0, z = a$ . The electric field in the region is given by $\vec{E} = E_{0} x \hat{i}$ . 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 $ϵ_{0} = 9 \times 10^{- 12} C^{2} / {Nm}^{2}$ ).

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answer is 288.

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Detailed Solution

Given, $\bar{E} = E_{0} x \hat{i} and E_{0} = 4 \times 10^{4} {Nc}^{- 1} m^{- 1}$
$a = 2 \times 10^{- 2} m$
Electric flux, $ϕ_{E} = \bar{E} \cdot \bar{A}$
$\begin{array}{l} \Rightarrow \frac{q}{ε_{0}} = EA \\ \Rightarrow q = ε_{0} EA \\ q = 9 \times 10^{- 12} \times 4 \times 10^{4} \times 2 \times 10^{- 2} \times 4 \times 10^{- 4} \\ q = 288 \times 10^{- 14} C \\ ∴ Q = 288 \end{array}$