Worked example: A classroom Van de Graaff has a dome of radius R = 0.15 m and the belt delivers I = 20 μA of charge. (a) What is the dome's capacitance? (b) How fast does the voltage rise? (c) Roughly what maximum voltage is expected before sparking to a nearby grounded object 0.3 m away? Step 1: C = 4πε0R = 4π(8.854 × 10⁻¹²)(0.15) ≈ 1.67 × 10⁻¹¹ F ≈ 17 pF. Step 2: dV/dt = I/C = (2 × 10⁻⁵)/(1.67 × 10⁻¹¹) ≈ 1.2 × 10⁶ V/s — over a million volts per second in the ideal case (leakage slows it). Step 3: Air breaks down at ~3 × 10⁶ V/m; across 0.3 m that is ~9 × 10⁵ V ≈ 0.9 MV. So expect dramatic sparks around a megavolt — matching the hair-raising classroom demos. Note the current is tiny (20 μA), so despite megavolts the shock is startling but not dangerous: energy = (1/2)CV² stays small.