Question

Question 1.23: An infinite line charge produces a field of 9 × 10 4 N/C at a distance of 2 cm. Calculate the linear charge density.

Class 12 - Physics - Electric Charges And Fields Electric Charges And Fields Page-48

Answer 1

infinite line charge produces a field , E = 9 × 10⁴ N/C at distance, r = 2cm = 0.02 m

as we know, electic field produced by line charge at distance r from the line charge is given by $\bf{E=\frac{\lambda}{2\pi\epsilon_0r}}$
so, $\bf{\lambda=2\pi\epsilon_0r.E}$

now, λ = 2 × 3.14 × 8.85 × 10^-12 × 0.02 × 9 × 10⁴
= 0.36 × 3.14 × 8.85 × 10^-8 C/m
≈ 1 × 10^-7 C/m

hence, linear charge density , λ = 10^-7 C/m