An infinite uniform line of linear charge density λ produces an electric field at perpendicular distance r equal to:

1. By Gauss's law with a cylindrical surface of radius r and length L: 2. E · 2π r L = (λ L) / ε₀. 3. E = λ / (2π ε₀ r). 4. Note 1/r dependence (not 1/r² — that's a point charge). _Source: syllabus Physics Ch 1 §1.10 Applications of Gauss's Law_