JEE PYQ: Electrostatics Question 41
Question 41 - 2019 (08 Apr Shift 2)
An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is:
(1) $\sqrt{\frac{qE}{md}}$
(2) $\sqrt{\frac{2qE}{md}}$
(3) $2\sqrt{\frac{qE}{md}}$
(4) $\sqrt{\frac{qE}{2md}}$
Show Answer
Answer: (2)
Solution
$\tau = -pE\sin\theta \approx -pE\theta$ for small $\theta$. $I\alpha = -qd \cdot E \cdot \theta$, where $I = 2m\left(\frac{d}{2}\right)^2 = \frac{md^2}{2}$. $\omega = \sqrt{\frac{pE}{I}} = \sqrt{\frac{qdE}{md^2/2}} = \sqrt{\frac{2qE}{md}}$.
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