An infinitely long wire has uniform linear charge density λ=2 nC / m . The net flux through a Gaussian cube of side length 3 ~cm , if the wire passes through any two corners of the cube, that are maximally displaced

Correct answer: D. 2.16 π aligned & φ= q_ enc _0 = λ · 3 a _0 & =2 × 10^ -9 × 3 × 3 × 10^ -2 × 36 π × 10^9 Nm^2 C^ -1 & =2.16 π Nm^2 C^ -1 aligned

JEE Main 20258 AprilEvening Shift

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An infinitely long wire has uniform linear charge density λ=2 nC /...

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]

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}