An electric dipole of dipole moment $\vec{p}$ is placed in a UNIFORM electric field $\vec{E}$. The torque experienced is
A$\vec{p} + \vec{E}$
B$\vec{p} \cdot \vec{E}$
C$\vec{p} \times \vec{E}$
D$|\vec{p}|\,|\vec{E}|\,\hat{r}$
Answer & Solution
Correct answer: C. $\vec{p} \times \vec{E}$
1. syllabus derives the torque on a dipole in a uniform field.
2. The two equal-and-opposite forces $\pm qE$ at the dipole ends form a COUPLE. Net force is zero, but the couple produces a torque.
3. The torque magnitude is $\tau = pE\sin\theta$, where $\theta$ is the angle between $\vec{p}$ and $\vec{E}$.
4. Direction: along $\vec{p}\times\vec{E}$ by the right-hand rule — perpendicular to the plane containing $\vec{p}$ and $\vec{E}$.
5. So vectorially $\vec{\tau} = \vec{p}\times\vec{E}$. The torque acts to ROTATE the dipole until $\vec{p} \parallel \vec{E}$ (stable equilibrium).
6. Option A has wrong dimensions. Option B is the scalar product (a number, not a vector). Option D is dimensionally wrong.
_Source: syllabus Physics Part 1, Ch 1, §1.10 (Dipole in a Uniform Field), p. 25._
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