Practice question
Question
A dipole with \( p = 3 \times 10^{-10} \, \text{C m} \) makes an angle of \( 90^\circ \) with a uniform
field \( E = 2 \times 10^5 \, \text{N/C} \). What is its potential energy?
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 = -3 × 10⁻¹⁰ × 2 × 10⁵ × cos 90° = 0 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 0 J follows, reflecting potential-capacitance relations.
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