Question

An infinite line charge produces a field of $9 × 10^4 NC^{-1}$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 $λ$ is given by the relation,
                                                          $E = \frac{λ}{2πε_0d}$
$λ = 2πε_0dE$
Where, d = 2 cm = 0.02 m
$E = 9 × 10^4 NC^{-1}$
$ε_0$ = Permittivity of free space and $\frac{1}{ 4πε_0} = 9 × 10^9 Nm^2C^{-2}$
Therefore,
                                                      $λ  =\frac{ 0.02 × 9 × 10^4 }{ 2 × 9× 10^9}$
$= 10\,µCm^{-1}$
Therefore, the linear charge density is $10\,µCm^{-1}$.