Worked example: (a) Find the capacitance of an isolated conducting sphere of radius 0.1 m. (b) A coaxial cable of length 10 m has inner radius 1 mm and outer radius 4 mm. Find its capacitance. Step 1: Isolated sphere: C = 4πε0R = 4π(8.854 × 10⁻¹²)(0.1) = 1.11 × 10⁻¹¹ F ≈ 11 pF. Step 2: Coaxial: C = 2πε0L/ln(b/a) = 2π(8.854 × 10⁻¹²)(10)/ln(4/1) = (5.563 × 10⁻¹⁰)/1.386 = 4.01 × 10⁻¹⁰ F ≈ 400 pF, i.e. ~40 pF/m. Step 3 (interpretation): The cable stores 40 times more charge per volt per metre than... actually compare fairly: per metre the cable is 40 pF/m while a 0.1 m sphere is 11 pF total — curved geometry packs capacitance efficiently into long runs, which is why kilometres of cable have microfarads of capacitance that round off fast pulses.