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°. Dipole moment: p = q × 2a = 3 × 10⁻⁶ × 5 × 10⁻³ = 1.5 × 10⁻⁸ C m . Torque: tau = p E sin θ = 1.5 × 10⁻⁸ × 8 × 10⁴ × sin 45° = 1.2 × 10⁻³ × (√(2)/2) = 8.48 × 10⁻⁴ N m . Substituting values gives 8.48 × 10⁻⁴ N m, which matches expected