Q 12-01-166JEE MainJEE Main 2025 (8 Apr, Shift 2)Medium
An infinitely long wire has uniform linear charge density $\lambda = 2\ \text{nC/m}$. The net flux through a Gaussian cube of side length $\sqrt3\ \text{cm}$, if the wire passes through two corners of the cube that are maximally displaced from each other, would be $x\ \text{N m}^2\text{C}^{-1}$, where $x$ is: (Neglect any edge effects and use $\dfrac1{4\pi\varepsilon_0} = 9\times10^9$ SI units)
Answer: (D) $2.16\pi$
The wire runs along a body diagonal of the cube, of length $\sqrt3a = \sqrt3\times\sqrt3 = 3\ \text{cm}$. The enclosed charge is $q = \lambda\times0.03\ \text{m}$.
$$\phi = \frac{q}{\varepsilon_0} = 4\pi\times9\times10^9\times2\times10^{-9}\times0.03 = 2.16\pi\ \text{N m}^2\text{C}^{-1}$$
Solution by Sreeraj P, M.Sc Physics