Worked example: A thin rod of length L = 0.5 m carries uniform linear charge λ = 4 μC/m. Find the total charge and the charge on its middle third. Step 1: Total Q = λL = (4 × 10⁻⁶)(0.5) = 2.0 × 10⁻⁶ C = 2.0 μC. Step 2: Because the distribution is uniform, charge scales with length: the middle third has length L/3, so Q_middle = λ·(L/3) = Q/3 ≈ 0.67 μC. Step 3 (density conversion practice): If this same 2.0 μC were spread uniformly over a spherical shell of radius 0.1 m, the surface density would be σ = Q/(4πR²) = (2.0 × 10⁻⁶)/(4π × 0.01) ≈ 1.59 × 10⁻⁵ C/m². The moral: always identify which density fits the geometry — line, surface, or volume — before writing dq.