An infinitely long wire has uniform linear charge density . The net flux through a Gaussian cube of side length , if the wire passes through any two corners of the cube, that are maximally displaced from each other would be , where x is: [Neglect any edge

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Solution

Q.
An infinitely long wire has uniform linear charge density $λ = 2 nC / m$ . The net flux through a Gaussian cube of side length $\sqrt{3} cm$ , if the wire passes through any two corners of the cube, that are maximally displaced from each other would be $x {Nm}^{2} C^{- 1}$ , where x is: [Neglect any edge effects and use $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} SI units$ ] [2025]

1 0.72 $π$

2 4.44 $π$

3 6.48 $π$

4 2.16 $π$

Ans.
(4)

$ϕ = \frac{q_{enclosed}}{ε_{0}}$

$l = \sqrt{3} a = 3 cm$

$q_{enclosed} = λ l$

$\Rightarrow ϕ = \frac{λ l}{ε_{0}}$

$= 2 \times 10^{- 9} \times 3 \times 10^{- 2} \times 4 π \times 9 \times 10^{9}$

$= 2.16 π$

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