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Question

A dipole with \( p = 4 \times 10^{-9} \, \text{C m} \) is at 30° to a field \( E = 6 \times 10^4 \,
\text{N/C} \). What is the torque?

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Explanation

**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. tau = p E sin θ . tau = 4 × 10⁻⁹ × 6 × 10⁴ × sin 30° = 24 × 10⁻⁵ × 0.5 = 1.2 × 10⁻⁴ N m . Substituting values gives 1.2 × 10⁻⁴ N m, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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