Practice question

**Continuous distribution** uses linear density λ = dq/dl (C/m), surface σ = dq/dA, volume ρ = dq/dV. Field of infinite line with uniform λ is E = 2kλ/r = λ/(2π ε₀ r) radially outward, derived via cylindrical Gaussian surface, showing 1/r dependence. Surface area: A = 4 π r² = 4 π (0.29)² = 0.335 π m² . Charge: q = sigma A = 50 × 10⁻⁶ × 0.335 π = 5.27 × 10⁻⁵ C . Substituting values gives 5.27 × 10⁻⁵ C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.