Question 269 of 311

An infinitely long wire has uniform linear charge density $\lambda=2 \mathrm{nC} / \mathrm{m}$. The net flux through a Gaussian cube of side length $\sqrt{3} \mathrm{~cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $\mathrm{xNm}^2 \mathrm{C}^{-1}$, where x is :
[Neglect any edge effects and use $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ SI units]

A$0.72 \pi$B$1.44 \pi$C$6.48 \pi$D$2.16 \pi$

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Answer: (D) $2.16 \pi$

$\begin{aligned} & \phi=\frac{\mathrm{q}_{\mathrm{enc}}}{\varepsilon_0}=\frac{\lambda \cdot \sqrt{3} \mathrm{a}}{\varepsilon_0} \\ & =2 \times 10^{-9} \times \sqrt{3} \times \sqrt{3} \times 10^{-2} \times 36 \pi \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1} \\ & =2.16 \pi \mathrm{Nm}^2 \mathrm{C}^{-1}\end{aligned}$