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. E = (2 k λ/r) , k = 9 × 10⁹ N·m²/C² . E = (2 × 9 × 10⁹ × 1.5 × 10⁻⁶/0.5) = 5.4 × 10⁴ N/C . Substituting values gives 5.4 × 10⁴ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.