Electric Field Due to Long Line Charge

A line charge is in the form of a thin charged wire of infinite length with a uniform linear charge density σ (charge per unit length).

φ_E = Σ E. ∆s

= E × 2πrl

According to Gauss' law

φ_E = q/ε₀

Hence

E × 2πrl = q/ε₀ = σl/ε₀

E = σ/(2πε₀r)

Electric field varies inversely with distance.