For an electric dipole in a non-uniform electric field with dipole moment parallel to direction of the field, the force F and torque \( \tau \) on the dipole respectively are ____________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( F \ne 0,\ \tau = 0 \)
The torque on a dipole is \( \vec{\tau} = \vec{p} \times \vec{E} \), so it depends only on the angle between \( \vec{p} \) and \( \vec{E} \). With \( \vec{p} \) parallel to \( \vec{E} \), the angle is zero and
\( \displaystyle \tau = pE\sin 0^\circ = 0 \)
The net force depends on whether the field is the same at the two charges. In a non-uniform field the field at \( +q \) differs from the field at \( -q \), so the forces \( q\vec{E}_{+} \) and \( -q\vec{E}_{-} \) do not cancel and \( F \ne 0 \).
Why the other options are incorrect
Option (1) \( F = 0,\ \tau = 0 \) — Incorrect. \( F = 0 \) holds only in a uniform field.
Option (3) \( F = 0,\ \tau \ne 0 \) — Incorrect. The torque is zero for a parallel dipole, and the force is not zero in a non-uniform field; both parts are wrong.
Option (4) \( F \ne 0,\ \tau \ne 0 \) — Incorrect. The torque vanishes because \( \vec{p} \) is parallel to \( \vec{E} \).
NCERT (2026-27):
Dipole in a Uniform External Field – “… The general case is involved, so let us consider the simpler situations when p is parallel to E or antiparallel to E. In either case, the net torque is zero, but there is a net force on the dipole if E is not uniform.”