JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Electrostatics

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 from each other, would be

xNm^{2} C^{- 1}

, where x is :
[Neglect any edge effects and use

\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9}

SI units]

Answer: (D)

Solution

When the wire runs along the body diagonal of the cube it joins the two most widely separated corners, so the length enclosed equals that diagonal,

3 a = 3 \times 3 cm = 3 cm

. The charge enclosed is

q = λ \times 0.03 = 2 \times 1 0^{- 9} \times 0.03 = 6 \times 1 0^{- 11} C

. By Gauss's law the flux is

ϕ = \frac{q}{ε _{0}} = q \times 4 π \times 9 \times 1 0^{9} = 6 \times 1 0^{- 11} \times 36 π \times 1 0^{9}

. The net flux through the cube is

2.16 π N m^{2} C^{- 1}

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option