An infinitely long line charge distribution produces a field of \( 9 \times 10^{4}\,\mathrm{N\,C^{-1}} \) at a distance of 2 cm. The linear charge density of the distribution is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.1\,\mu\mathrm{C\,m^{-1}} \)
The field of an infinite line charge of linear density \( \lambda \), at distance \( r \), is
\( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0\,r} = \frac{2k\lambda}{r} \)
\( k = 9\times10^{9}\,\mathrm{N\,m^2\,C^{-2}} \)
\( r = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \displaystyle \lambda = \frac{E\,r}{2k} = \frac{9\times10^{4} \times 0.02}{2 \times 9\times10^{9}} = 10^{-7}\,\mathrm{C\,m^{-1}} = 0.1\,\mu\mathrm{C\,m^{-1}} \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
