Practice question

**Interaction of dipole with uniform field** produces pure couple without net force, equal opposite forces forming torque. Potential energy minimum -pE at alignment, maximum +pE at anti-alignment, governing orientation dynamics. Dipole moment: p = q × 2a = 5 × 10⁻⁶ × 3 × 10⁻³ = 1.5 × 10⁻⁸ C m . Torque: tau = p E sin θ = 1.5 × 10⁻⁸ × 2 × 10⁴ × sin 45° = 3 × 10⁻⁴ × (√(2)/2) = 2.12 × 10⁻⁴ N m . Substituting values gives 2.12 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.