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Question

A dipole with charges \( +2 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) separated by 1 mm is in a
field of \( 6 \times 10^4 \, \text{N/C} \) at 90°. What is the torque?

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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 = 2 × 10⁻⁶ × 1 × 10⁻³ = 2 × 10⁻⁹ C m . Torque: tau = p E sin θ = 2 × 10⁻⁹ × 6 × 10⁴ × sin 90° = 1.2 × 10⁻⁴ N m . Substituting values gives 1.2 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming

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