A dipole is placed in a uniform electric field. Its potential energy will be minimum when the angle between its axis and electric field is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Zero
The potential energy of a dipole in a uniform field is
\( U = -\vec{p}\cdot\vec{E} = -pE\cos\theta \)
It is least (most negative) when \( \cos\theta = 1 \), i.e. when the dipole points along the field.
\( \theta = 0: U = -pE\ \text{(minimum)} \)
\( \theta = \pi/2: U = 0 \)
\( \theta = \pi: U = +pE\ \text{(maximum)} \)
At \( \theta = 0 \) the dipole is in stable equilibrium.
Note: A similar question was also asked in CUET (UG) 2025 on 13-05-2025 (Slot 1).
NCERT (2026-27):
Potential Energy of a Dipole in an External Field – “… This work is stored as the potential energy of the system. We can then associate potential energy \( U(\theta) \) with an inclination \( \theta \) of the dipole. … A natural choice is to take \( \theta_0 = \pi/2 \). … We can then write,
\( \displaystyle U(\theta) = pE\left(\cos\frac{\pi}{2} - \cos\theta\right) = -pE\cos\theta = -\mathbf{p}\cdot\mathbf{E} \qquad (2.32) \)”