An electric dipole is placed in a uniform electric field. Each of its two charges feels a force of \(2\times10^{-3}\ \mathrm{N}\). The charges are 4 cm apart, and the dipole axis makes an angle of \(30^\circ\) with the field. The magnitude of the torque on the dipole is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(4.0\times10^{-5}\ \mathrm{N\,m}\)
The forces \( qE \) and \( -qE \) on the two charges are equal and opposite, so they form a couple. The torque is the size of one force times the perpendicular distance between the two forces, \( \tau=qE\times2a\sin\theta \).
Given:
\( qE=2\times10^{-3}\ \mathrm{N} \)
\( 2a=4\ \mathrm{cm}=0.04\ \mathrm{m} \)
\( \theta=30^\circ \)
\( \begin{aligned} \tau &= qE\times2a\sin\theta \\ &= 2\times10^{-3}\times0.04\times\sin30^\circ \\ &= 4.0\times10^{-5}\ \mathrm{N\,m} \end{aligned} \)
NCERT (2026-27):
Dipole in a Uniform External Field – “There is a force qE on q and a force –qE on –q. … Its magnitude equals the magnitude of each force multiplied by the arm of the couple (perpendicular distance between the two antiparallel forces). Magnitude of torque = q E × 2 a sinθ = 2 q a E sinθ”