A thin infinite line charge has linear charge density of \( 2.0\times10^{-9}\,\mathrm{C\,m^{-1}} \). The electric field intensity at a distance of 3 m from the line charge is: \( \left(\displaystyle\frac{1}{4\pi\varepsilon_0} = 9\times10^{9}\right) \)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 12\,\mathrm{N\,C^{-1}} \)
By Gauss's law applied to a cylinder around the line, the field of an infinitely long line charge of density \( \lambda \) at a distance r is
\( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0 r} = \frac{2}{4\pi\varepsilon_0}\,\frac{\lambda}{r} \)
\( \displaystyle E = 2\times9\times10^{9}\times\frac{2.0\times10^{-9}}{3} = 12\,\mathrm{N\,C^{-1}} \)