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(A) When an electric dipole of dipole moment $p$ is placed in a uniform electric field $E$,the restoring torque acting on it for a small angular displ

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) When an electric dipole of dipole moment $p$ is placed in a uniform electric field $E$,the restoring torque acting on it for a small angular displacement $	heta$ is given by $	au = -pE \sin 	heta$. For small angles,$\sin 	heta \approx 	heta$,so $	au = -pE 	heta$. Using the rotational analog of Newton's second law,$	au = I \alpha$,where $\alpha = \frac{d^2 	heta}{dt^2}$ is the angular acceleration. Thus,$I \frac{d^2 	heta}{dt^2} = -pE 	heta$,which simplifies to $\frac{d^2 	heta}{dt^2} = -(\frac{pE}{I}) 	heta$. This is the equation of simple harmonic motion $\frac{d^2 	heta}{dt^2} = -\omega^2 	heta$. Comparing the two,we get $\omega^2 = \frac{pE}{I}$,so the angular frequency is $\omega = (\frac{pE}{I})^{1/2}$.

An electric dipole is situated in a uniform electric field of intensity $E$. The dipole moment is $p$ and the 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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