Electric Charges and Fields - Result Question 25
25. If a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then torque acting on it is given by
[2001]
(a) $\vec{\tau}=\vec{p} \cdot \vec{E}$
(b) $\vec{\tau}=\vec{p} \times \vec{E}$
(c) $\vec{\tau}=\vec{p}+\vec{E}$
(d) $\vec{\tau}=\vec{p}-\vec{E}$
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Answer:
Correct Answer: 25. (b)
Solution:
- (b) Given : Dipole moment of the dipole $=\vec{p}$ and uniform electric field $=\vec{E}$. We know that dipole moment $(p)=q \cdot a$ (where $q$ is the charge and $a$ is dipole length). And when a dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, then Torque $(\tau)=$ Either force $\times$ Perpendicular distance between the two forces $=$ $q a E \sin \theta$ or $\tau=p E \sin \theta$ or $\vec{\tau}=\vec{p} \times \vec{E}$ (vector form)
