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Question

A dipole \( p = 4 \times 10^{-10} \, \text{C m} \) is in a uniform field \( E = 10^5 \, \text{N/C} \)
at \( 60^\circ \). What is its potential energy?

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Explanation

**Equipotential through midpoint** of +q and -q is perpendicular bisector, V=0 everywhere on it because contributions k q/r and k(-q)/r cancel. For two opposite charges, potential at midpoint zero, but field non-zero, pointing from positive to negative, illustrating vector vs scalar nature. U = -p · E = -p E cos θ = -4 × 10⁻¹⁰ × 10⁵ × cos 60° = -4 × 10⁻⁵ × 0.5 = -2 × 10⁻⁵ J . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V = Q_total/C_total, result

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