Question
An electric dipole with dipole moment $5 \times 10^{- 6}Cm$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^{5}\text{ }N/C$. The dipole is then rotated through an angle of $60^{\circ}$ with respect to the electric field. The change in the potential energy of the dipole is:
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Solution
Given
$$\begin{matrix} & \ |\overrightarrow{P}| = 5 \times 10^{- 6}Cm \\ & \ |\overrightarrow{E}| = 4 \times 10^{5}\text{ }N/C \\ & \theta_{i} = 0^{\circ}\text{~}\text{and}\text{~}\theta_{f} = 60^{\circ} \\ & \Delta U = U_{f} - U_{i} \\ & \ = - PEcos\theta_{f} + PEcos\theta_{i} \\ & \ = PE\left\lbrack cos\theta_{i} - cos\theta_{f} \right) \\ & \ = 5 \times 10^{- 6} \times 4 \times 10^{5}\left( 1 - \frac{1}{2} \right) \\ & \ = 10 \times 10^{- 6} \times 10^{5} = 1\text{ }J \end{matrix}$$
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