The linear charge density of an infinite line charge producing a uniform electric field of \( 9\times10^{6}\,\mathrm{N/C} \) at a distance of 2 cm is :
(Take permittivity of vacuum \( \epsilon_0 = 8.85\times10^{-12}\,\mathrm{C^2\,N^{-1}\,m^{-2}} \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 10\,\mu\mathrm{C/m} \)
By Gauss's law applied to a cylinder around the line, the field of an infinite line charge at distance \( r \) is
\( \displaystyle E = \frac{\lambda}{2\pi\epsilon_0\,r} \;\Rightarrow\; \lambda = 2\pi\epsilon_0\,r\,E \)
\( r = 2\,\mathrm{cm} = 0.02\,\mathrm{m} \)
\( \displaystyle \lambda = 2\pi \times 8.85\times10^{-12} \times 0.02 \times 9\times10^{6} \)
\( \displaystyle \lambda = 2\pi \times 1.593\times10^{-6} \approx 1.0\times10^{-5}\,\mathrm{C/m} = 10\,\mu\mathrm{C/m} \)
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 – …
