An infinite line charge produces an electric field of \( 9 \times 10^{6}\,\mathrm{N/C} \) at a distance of 20 cm. The linear charge density will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 10^{-4}\,\mathrm{C/m} \)
By Gauss's law applied to a cylinder around an infinite line charge, the field at distance \( r \) is
\( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0\,r} = \frac{2k\lambda}{r}, \quad k = \frac{1}{4\pi\varepsilon_0} = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \)
So the linear charge density is
\( \displaystyle \lambda = \frac{E\,r}{2k} \)
\( E = 9\times10^{6}\,\mathrm{N\,C^{-1}} \)
\( r = 20\,\mathrm{cm} = 0.2\,\mathrm{m} \)
\( \displaystyle \lambda = \frac{9\times10^{6} \times 0.2}{2 \times 9\times10^{9}} = \frac{1.8\times10^{6}}{1.8\times10^{10}} = 10^{-4}\,\mathrm{C\,m^{-1}} \)
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 – …
