An electric dipole is made of charges \(+2\ \mu\mathrm{C}\) and \(-2\ \mu\mathrm{C}\) placed 3 cm apart. It is held in a uniform electric field of \(2\times10^{5}\ \mathrm{N\,C^{-1}}\), with its axis at right angles to the field. The net force and the torque on the dipole are, respectively,
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → zero and \(1.2\times10^{-2}\ \mathrm{N\,m}\)
In a uniform field the charge \( +q \) feels a force \( qE \) along the field, and \( -q \) feels an equal force opposite to it. These two forces add up to zero, but they act at different points. So they form a couple and turn the dipole. Its torque is \( \tau=pE\sin\theta \), with \( p=q\times2a \).
Given:
\( q=2\times10^{-6}\ \mathrm{C} \)
\( 2a=3\ \mathrm{cm}=0.03\ \mathrm{m} \)
\( E=2\times10^{5}\ \mathrm{N\,C^{-1}} \)
\( \theta=90^\circ \)
\( \begin{aligned} p &= q\times2a \\ &= 2\times10^{-6}\times0.03 \\ &= 6\times10^{-8}\ \mathrm{C\,m} \end{aligned} \)
\( \begin{aligned} \tau &= pE\sin90^\circ \\ &= 6\times10^{-8}\times2\times10^{5}\times1 \\ &= 1.2\times10^{-2}\ \mathrm{N\,m} \end{aligned} \)
Each charge feels a force of \( qE=0.4\ \mathrm{N} \), but the two forces point in opposite directions. Therefore, the net force is zero and only the torque acts.
NCERT (2026-27):
Dipole in a Uniform External Field – “There is a force qE on q and a force –qE on –q. The net force on the dipole is zero, since E is uniform. However, the charges are separated, so the forces act at different points, resulting in a torque on the dipole. … Magnitude of torque = q E × 2 a sinθ = 2 q a E sinθ”