An electric dipole of dipole moment \(6\times10^{-9}\ \mathrm{C\,m}\) is held in a uniform electric field of \(2\times10^{4}\ \mathrm{N\,C^{-1}}\), with its dipole moment at \(60^\circ\) to the field. Taking the potential energy to be zero when the dipole is at right angles to the field, the potential energy of the dipole is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-6\times10^{-5}\ \mathrm{J}\)
With the zero of energy at \( \theta=90^\circ \), a dipole in a uniform field has potential energy \( U=-pE\cos\theta \). For any angle less than \( 90^\circ \) this energy is negative.
\( \begin{aligned} U &= -pE\cos60^\circ \\ &= -6\times10^{-9}\times2\times10^{4}\times0.5 \\ &= -6\times10^{-5}\ \mathrm{J} \end{aligned} \)
NCERT (2026-27):
Potential energy of a dipole in an external field – “A natural choice is to take θ0 = π / 2.”
Summary – “The potential energy of a dipole moment p in a uniform electric field E is –p.E.”