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Question

A dipole with \( p = 5 \times 10^{-9} \, \text{C m} \) makes an angle of \( 30^\circ \) with a uniform
field \( E = 3 \times 10^5 \, \text{N/C} \). What is its potential energy?

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Explanation

**Sign of potential energy** indicates nature of interaction, like charges U>0, opposite U<0. Work done by field moving positive charge from higher to lower potential positive, as field does work W = q ΔV, ΔV negative when moving to lower V. U = -p E cos θ = -5 × 10⁻⁹ × 3 × 10⁵ × cos 30° . cos 30° = (√(3)/2) ≈ 0.866 , so U = -5 × 10⁻⁹ × 3 × 10⁵ × 0.866 = -1.299 × 10⁻³ J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U

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