An infinitely long line charge produces an electric field of 9 × 104…

The correct answer is Option (1) → 10 μC/m

By Gauss’s law applied to a cylinder around the line, the field of an infinitely long line charge falls off as 1/r:

    \( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0 r} \)

    \( \displaystyle \lambda = 2\pi\varepsilon_0 r E = \frac{rE}{2 \times 9\times10^{9}} \)

    \( \displaystyle \lambda = \frac{2\,\mathrm{m} \times 9\times10^{4}\,\mathrm{N\,C^{-1}}}{2 \times 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}}} \)

    \( \lambda = 1\times10^{-5}\,\mathrm{C\,m^{-1}} = 10\,\mu\mathrm{C\,m^{-1}} \)

Here \( 2\pi\varepsilon_0 = 1/(2 \times 9\times10^{9}) \), since \( 1/4\pi\varepsilon_0 = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \).

Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.

NCERT (2026-27):
Exercises – …