An electric dipole of dipole moment \(3\times10^{-9}\ \mathrm{C\,m}\) is placed in a uniform electric field of \(2\times10^{4}\ \mathrm{N\,C^{-1}}\). List-I gives the angle between the dipole moment and the field. Match List-I with the magnitude of the torque on the dipole in List-II.
| List-I | List-II |
|---|---|
| (A) \(0^\circ\) | (I) \(6\times10^{-5}\ \mathrm{N\,m}\) |
| (B) \(30^\circ\) | (II) \(5.2\times10^{-5}\ \mathrm{N\,m}\) |
| (C) \(60^\circ\) | (III) \(3\times10^{-5}\ \mathrm{N\,m}\) |
| (D) \(90^\circ\) | (IV) Zero |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
In a uniform field the torque on a dipole has magnitude \( \tau=pE\sin\theta \), where \( \theta \) is the angle between \( \vec p \) and \( \vec E \). The largest torque is \( pE \).
\( \begin{aligned} pE &= 3\times10^{-9}\times2\times10^{4} \\ &= 6\times10^{-5}\ \mathrm{N\,m} \end{aligned} \)
(A) \(0^\circ\) — This matches (IV) zero. Here \( \sin0^\circ=0 \), so the dipole is aligned with the field and feels no torque.
(B) \(30^\circ\) — This matches (III). With \( \sin30^\circ=0.5 \), the torque is \( 3\times10^{-5}\ \mathrm{N\,m} \).
(C) \(60^\circ\) — This matches (II). With \( \sin60^\circ\approx0.87 \), the torque is about \( 5.2\times10^{-5}\ \mathrm{N\,m} \).
(D) \(90^\circ\) — This matches (I). With \( \sin90^\circ=1 \), the torque has its largest value \( 6\times10^{-5}\ \mathrm{N\,m} \).
NCERT (2026-27):
Dipole in a Uniform External Field – “… The magnitude of p × E is also p E sinθ …”
Dipole in a Uniform External Field – “This torque will tend to align the dipole with the field E. When p is aligned with E, the torque is zero.”