An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced then the angular frequency of its oscillation is :

(\frac{p E}{I})^{\frac{1}{2}}

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(\frac{p E}{I})^{\frac{3}{2}}

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(\frac{I}{p E})^{\frac{1}{2}}

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(\frac{p}{I E})^{\frac{1}{2}}

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Solution

The correct option is A $(\frac{p E}{I})^{\frac{1}{2}}$
When the electric dipole is placed in a electric field in equilibrium position is displaced by small angle $θ$ , then it executes S.H.M due to restoring couple
$C = - p \in sin θ θ \approx$ small
$C = - p \in θ$
$C = I α = I \frac{d^{2} θ}{d t^{2}}$
$I \frac{d^{r} θ}{d t^{2}} = - p \in θ$
$\frac{d^{2} θ}{d t^{2}} = - \frac{p \in}{I} θ$
$\frac{d^{2} θ}{d t^{2}} = - w^{2} θ$
standard equation of SHM
$w = \sqrt{\frac{p \in}{I}}$
$V = \frac{w}{2 π} = \frac{1}{2 π} \sqrt{p \in} I$

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