An electric dipole of moment vec{P} is placed | vedclass

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Question

(A) The dipole experiences a restoring torque $	au = -pE \sin 	heta$ tending to bring it back in the direction of the field.For small angular displa

Vedclass · Accepted Answer

$2\pi \sqrt{I/pE}$

Vedclass · Answer

(A) The dipole experiences a restoring torque $	au = -pE \sin 	heta$ tending to bring it back in the direction of the field.For small angular displacements $	heta$, $\sin 	heta \approx 	heta$. Thus, the torque is $	au = -pE 	heta$.Using the rotational form of Newton's second law, $	au = I \alpha = I (d^2 	heta / dt^2)$.Equating the two expressions for torque: $I (d^2 	heta / dt^2) = -pE 	heta$.Rearranging gives $d^2 	heta / dt^2 = -(pE / I) 	heta$.Comparing this with the standard $S.H.M.$ equation $d^2 	heta / dt^2 = -\omega^2 	heta$, we find $\omega^2 = pE / I$, so $\omega = \sqrt{pE / I}$.The time period $T$ is given by $T = 2\pi / \omega = 2\pi \sqrt{I / pE}$.

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