Practice question

**System of charges** potential energy is sum over pairs U = Σ k q_i q_j/r_ij, work required to assemble charges from infinity. For 28 μC and -14 μC, 0.28 m apart, U=9×10⁹×28×(-14)×10⁻¹²/0.28= -12.6 J, negative indicates bound system. U = (1/4 π ε₀) (q₁ q₂/r) = 9 × 10⁹ × (15 × 10⁻⁶ × (-5 × 10⁻⁶)/0.12) . U = 9 × 10⁹ × (-75 × 10⁻¹²/0.12) = -5.625 J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V = Q_total/C_total, result -5.625 J follows, reflecting potential-capacitance relations.