An infinite line charge produces a field of $9 imes 10^4 ext{ N/C}$ at a distance of $2 ext{ cm}

Question

An infinite line charge produces a field of $9 	imes 10^4	ext{ N/C}$ at a distance of $2	ext{ cm}$. Calculate the linear charge density.

Professor PC Thomas Classes · Answer

Electric field for line charge is $E = \frac{\lambda}{2\pi\epsilon_0 r} = \frac{2k\lambda}{r}$. So $\lambda = \frac{E r}{2k} = \frac{9 	imes 10^4 	imes 0.02}{2 	imes 9 	imes 10^9} = \frac{1800}{18 	imes 10^9} = 10^{-7}	ext{ C/m} = 0.1\mu C/m$.