Electric Flux & Gauss's Law question from JEE Main 2021 (16 Mar, Shift 2)

Answer: (a)

1. Here 'surface charge density' means electric flux density $D = \varepsilon_0 E$ at the point.
2. For a line charge, $E = \frac{\lambda}{2\pi\varepsilon_0 r}$, so $D = \frac{\lambda}{2\pi r}$.
3. $D = \frac{8}{2\pi \times 3} = 0.424$ nC m$^{-2}$
4. So the answer is (a) 0.424 nC m$^{-2}$.