Question

An infinite line charge produces an electric field of $9\times {10}^{4}N{C}^{-1}$ at a distance of 2 cm. Calculate the linear charge density.

Answer 1

Electric field produced by the infinite line charges at a distance d having linear charge density $\lambda$ is given by the relation,
$E=\frac{\lambda }{2\pi {ϵ}_{0}d}$
$\lambda =2\pi {ϵ}_{0}dE$
Where,
D = 2 cm = 0.02 m
$E=9\times 104N/C$
${ϵ}_0$ = Permittivity of free space
$\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{m}^2{C}^{-2}$
$\lambda =\frac{0.02\times 9\times {10}^4}{2\times 9\times {10}^9}$
$=10\mu C/m$
Therefore, the linear charge density is $10\mu C/m$.