Question

An infinite line charge produces an electric field of $9.0\times {10}^4$N $C^{-1}$ at a distance of $2.0$cm. What is the linear charge density?

Answer 1

$E=\frac{\lambda }{\left(2\pi ϵor\right)}=\frac{2\lambda }{\left(4\pi ϵor\right)}$

$E=\frac{9\times 104N}{C}$

$\frac{1}{\left(4\pi ϵo\right)}=\frac{9\times 109N{m}^2}{C^2}$

Linear charge density$\lambda =\frac{E.4\pi ϵor}{2}$

$=\frac{(9\times {10}^4\frac{N}{C})(2\times {10}^{-}2)}{\left(\right(9\times 109\frac{{Nm}^2}{C^2})\times 2)}$

$=10-7\frac{C}{m}$