Practice question

**Dipole moment** governs torque and energy in external field. Axial field stronger than equatorial, torque maximum at θ = 90°, zero when aligned. Work done rotating dipole relates to ΔU = pE(1 - cosθ), explaining stable equilibrium at θ = 0°. Let x be distance from +9 μC , then 0.45 - x from -6 μC . (9 × 10⁻⁶/x²) = (6 × 10⁻⁶/(0.45 - x)²) , 9 (0.45 - x)² = 6 x² . 1.5 (0.2025 - 0.9 x + x²) = x² , 0.30375 - 1.35 x + 1.5 x² = x² . 0.5 x² - 1.35 x + 0.30375 = 0 ,