An electric dipole of moment $p$ is placed at $60°$ to a uniform electric field of magnitude $E$. The torque on the dipole is:
A$pE$
B$pE/2$
C$\sqrt{3}\,pE$
D$\dfrac{\sqrt{3}}{2}\,pE$
Answer & Solution
Correct answer: D. $\dfrac{\sqrt{3}}{2}\,pE$
**Torque on a dipole.** $\tau = pE \sin\theta$, where $\theta$ is the angle between the dipole moment and the field.
**Substitute.** With $\theta = 60°$, $\sin 60° = \dfrac{\sqrt 3}{2}$, so $\tau = \dfrac{\sqrt 3}{2}\,pE$.
**Distractor logic.** Option B uses $\cos 60° = 1/2$ instead of $\sin$. Option A is the maximum torque (would need $\theta = 90°$). Sine, not cosine — the torque is zero when the dipole *aligns* with the field, so it must use $\sin\theta$.
Related questions
If a positive point charge is placed at the centre of a spherical conducting shell of radiThe SI unit of electric field isFor a charge distribution with volume density ρ, the total charge Q equalsThe electric flux through a closed surface enclosing a charge of +5 μC is (ε₀ = 8.85 × 10⁻Two charges +q and −q of equal magnitude are placed at the corners A and B of an equilaterThe principle of quantisation of electric charge is stated asAn electric dipole in a uniform electric field E experiencesThe electric field on the axial line of a short electric dipole at distance r is