An electric dipole of dipole moment \( \vec{p} \) is aligned in the direction of a uniform electric field \( \vec{E} \). The work done in rotating the dipole from stable to unstable equilibrium state is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 2\,PE \)
The potential energy of a dipole in a uniform field is \( U = -pE\cos\theta \). Stable equilibrium is \( \theta = 0^\circ \) and unstable equilibrium is \( \theta = 180^\circ \).
The work done by an external agent in rotating the dipole slowly equals the increase in potential energy:
\( W = U_{180^\circ} - U_{0^\circ} \)
\( W = (-pE\cos180^\circ) - (-pE\cos0^\circ) \)
\( W = pE + pE = 2pE \)
Note: It seems that there is a mistake in the original NTA paper, which prints the dipole moment as a capital \( P \) in the options (\( PE \)) when the question uses \( \vec{p} \). The options clearly stand for the product \( pE \), so the question can still be solved.