An infinitely long wire has uniform linear charge density =2 nC /… - Vidyadip

MCQ

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
$6.48 \pi$
✓
$2.16 \pi$

✓

Answer

Correct option: D.

$2.16 \pi$

(D) $2.16 \pi$

$\phi=\frac{\mathrm{q}_{\mathrm{enc}}}{\varepsilon_{0}}=\frac{\lambda \cdot \sqrt{3 \mathrm{a}}}{\varepsilon_{0}}$
$=2 \times 10^{-9} \times \sqrt{3} \times \sqrt{3} \times 10^{-2} \times 36 \pi \times 10^{9} \mathrm{Nm}^{2} \mathrm{C}^{-1}$
$=2.16 \pi \mathrm{Nm}^{2} \mathrm{C}^{-1}$

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