An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90◦ is ?

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90◦  is ?

(a) \( p E^2 \)

(b) \( p^2 E \)

(c) \( p E \)

(d) \( \infty \)

Answer :  (c) \( p E \)

Rotational Potential Energy

\( U = -pE \cos \theta \)

\( \quad = -pE \cos 0^\circ \)

\( \quad = -pE \)

Work

\( W = U_2 - U_1 \)

\( \quad = -pE \cos \theta_2 - (-pE \cos \theta_1) \)

\( \quad = pE (\cos \theta_1 - \cos \theta_2) \)

\( \quad = pE (\cos 0^\circ - \cos 90^\circ) \)

\( \quad = pE (1 - 0) \)

\( \quad = pE \)