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(A) When an electric dipole is placed in a uniform electric field $E$,it experiences a torque $	au = pE \sin 	heta$. For a small angular displacemen

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$(\frac{pE}{I})^{1/2}$

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(A) When an electric dipole is placed in a uniform electric field $E$,it experiences a torque $	au = pE \sin 	heta$. For a small angular displacement $	heta$ from the equilibrium position,$\sin 	heta \approx 	heta$. Thus,the restoring torque is $	au = -pE	heta$. Using Newton's second law for rotation,$	au = I \alpha = I \frac{d^2	heta}{dt^2}$. Equating the two expressions: $I \frac{d^2	heta}{dt^2} = -pE	heta$. Rearranging gives $\frac{d^2	heta}{dt^2} = -(\frac{pE}{I})	heta$. Comparing this with the standard simple harmonic motion equation $\frac{d^2	heta}{dt^2} = -\omega^2 	heta$,we get $\omega^2 = \frac{pE}{I}$. Therefore,the angular frequency is $\omega = \sqrt{\frac{pE}{I}}$.

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 slightly from the equilibrium position,then the angular frequency of its oscillations is

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