Practice question
Question
A dipole \( p = 3 \times 10^{-9} \, \text{C m} \) is rotated from \( \theta = 0^\circ \) to \(
180^\circ \) in a field \( E = 4 \times 10^5 \, \text{N/C} \). What is the work done?
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. Work done: W = p E (cos θ₀ - cos θ₁) = 3 × 10⁻⁹ × 4 × 10⁵ × (cos 0° - cos 180°) . W = 3 × 10⁻⁹ × 4 × 10⁵ × (1 - (-1)) = 3 × 10⁻⁹ × 4 × 10⁵ × 2 = 2.4 × 10⁻³ J . Using V = kQ/r, U = k q₁q₂/r, E
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