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 $ω$ is

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$\sqrt{\frac{2 q E}{m d}}$

$\sqrt{\frac{q E}{m d}}$

$\sqrt{\frac{qE}{md}}$

$\sqrt{\frac{q E}{2 m d}}$

answer is B.

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Detailed Solution

$τ = - PEsin θ$
or $Iα = - PE (θ)$

$α = \frac{PE}{I} (- θ)$

On comparing with $α = - ω^{2} θ$

$ω = \sqrt{\frac{PE}{I}} = \sqrt{\frac{qdE}{2 m {(\frac{d}{2})}^{2}}} = \sqrt{\frac{2 qE}{md}}$

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