Practice question

**Applications** include charge sharing for voltage division, Van de Graaff generator accumulates charge on spherical dome to high potential V = k Q/R, up to MV, using belt to transport charge, capacitance of sphere C=4π ε₀ R ≈10 pF for R=0.1 m, so Q= C V ≈10⁻⁸ C for 1000 V. Initial energy: U_i = (1/2) × 3 × 10⁻⁶ × (200)² = 0.06 J . Charge: Q = 3 × 10⁻⁶ × 200 = 6 × 10⁻⁴ C . Total C = 3 + 9 = 12 μF , V = (6 × 10⁻⁴/12 × 10⁻⁶) = 50 V . Final energy: U_f =