An electric dipole with dipole moment P and m | vedclass

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Question

(A) The torque acting on an electric dipole in a uniform electric field is given by $	au = PE \sin 	heta$.For small oscillations,$\sin 	heta \appro

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The torque acting on an electric dipole in a uniform electric field is given by $	au = PE \sin 	heta$.For small oscillations,$\sin 	heta \approx 	heta$,so $	au = PE 	heta$.Since the torque is restoring,$	au = -PE 	heta$.Using the rotational analog of Newton's second law,$	au = I \alpha$,where $\alpha$ is the angular acceleration.Therefore,$I \alpha = -PE 	heta$,which gives $\alpha = -(\frac{PE}{I}) 	heta$.Comparing this with the standard equation for simple harmonic motion,$\alpha = -\omega^2 	heta$,we get $\omega^2 = \frac{PE}{I}$.Thus,the angular frequency of oscillation is $\omega = \sqrt{\frac{PE}{I}}$.

Column-$I$ (Angle between $\vec{p}$ and $\vec{E}$)	Column-$II$ (Potential energy of the dipole)
$a. 180^{\circ}$	$i. -pE$
$b. 120^{\circ}$	$ii. pE$
$c. 90^{\circ}$	$iii. \frac{1}{2} pE$
	$iv. 0$

An electric dipole with dipole moment $P$ and moment of inertia $I$ is placed in a uniform electric field of intensity $E$. If the dipole is slightly rotated,the angular frequency of its oscillation is ........

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