An electric dipole of dipole moment \( \vec{p} \) is rotated in an electric field of magnitude E from the most stable orientation to most unstable orientation. The work done in the process is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2pE \)
The potential energy of a dipole in a uniform field depends on the angle \( \theta \) between \( \vec{p} \) and \( \vec{E} \). The work done by the external agent in rotating it slowly equals the change in potential energy.
\( \displaystyle U = -pE\cos\theta \)
The most stable orientation is \( \theta = 0^\circ \) (minimum energy) and the most unstable orientation is \( \theta = 180^\circ \) (maximum energy).
\( U_{i} = -pE\cos 0^\circ = -pE \)
\( U_{f} = -pE\cos 180^\circ = +pE \)
\( \displaystyle W = U_{f} - U_{i} = pE - (-pE) = 2pE \)