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Question

A dipole has charges \( +q = 3 \, \mu\text{C} \) and \( -q = -3 \, \mu\text{C} \) separated by 2 mm.
What is the dipole moment?

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Explanation

**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 , where 2a = 2 × 10⁻³ m , q = 3 × 10⁻⁶ C . p = 3 × 10⁻⁶ × 2 × 10⁻³ = 6 × 10⁻⁹ C m . Substituting values gives 6 × 10⁻⁹ C m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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