A dipole with dipole moment p and moment of i | vedclass

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Question

(B) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by $	au = p E \sin 	heta$,where $p$ is the electric dipo

Vedclass · Accepted Answer

$2 \pi \sqrt{\frac{I}{p E}}$

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(B) The torque $	au$ on an electric dipole placed in a uniform electric field $E$ is given by $	au = p E \sin 	heta$,where $p$ is the electric dipole moment and $	heta$ is the angle between $p$ and $E$.For small angles $	heta$,we can approximate $\sin 	heta \approx 	heta$.Thus,the torque becomes $	au = p E 	heta$.Since the torque is also given by $	au = I \alpha$,where $I$ is the moment of inertia and $\alpha$ is the angular acceleration,we have $I \alpha = p E 	heta$.Rearranging for angular acceleration,we get $\alpha = \frac{p E}{I} 	heta$.This equation is of the form $\alpha = -\omega^2 	heta$,which represents simple harmonic motion.Comparing the terms,we find $\omega^2 = \frac{p E}{I}$,so $\omega = \sqrt{\frac{p E}{I}}$.The time period $T$ is given by $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{I}{p E}}$.

$A$ dipole with dipole moment $p$ and moment of inertia $I$ is placed in a uniform electric field $E$. If it is displaced slightly from its stable equilibrium position,the period of oscillation of the dipole is

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