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 \(10\,µCm^{-1}\).