Question

An infinite linear charge at $2cm$ distance produces an electric field of $9\times {10}^{4}N/C$. Determine the linear charge density.

Answer 1

Electric field intensity due to linear charge of infinite extension
$E=\frac{1}{4\pi {ϵ}_0}\frac{2\lambda }{r}$
Where $\lambda$ is linear charge density and r is distance of observation point from charge . according to question
$r=2cm=2\times {10}^{-2}m$
$\lambda =?,E=9\times {10}^{4}N{C}^{-1}$
$\therefore 9\times {10}^4=9\times {10}^9\times \frac{2\lambda }{2\times {10}^{-2}}$
$\therefore \gamma =1.0\times {10}^{-7}C{m}^{-1}$
$\Rightarrow \lambda =0.1\times {10}^{-6}=0.1\mu C{m}^{-1}$