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An electric dipole of dipole moment P is placed in a uniform electric field E in stable equilibrium position . It's moment of inertia about the centroidal axis is I . If it is displaced slightly from it mean position find the period of small oscillations .

$(a)\;2\pi \sqrt{\large\frac{I}{PE}}\qquad(b)\;\pi \sqrt{\large\frac{I}{PE}}\qquad(c)\;\pi \sqrt{\large\frac{PE}{I}}\qquad(d)\;2\pi \sqrt{\large\frac{PE}{I}}$

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Answer : (a) $\;2\pi \sqrt{\large\frac{I}{PE}}$
Explanation :
When displaced at an angle $\;theta$, from its mean position the magnitude of restoring torque is
$\tau=-P sin \theta$
For small angular displacement $\;sin \theta \approx \theta$
$\tau=-P E \theta$
$\alpha =\large\frac{\tau}{I}=-(\large\frac{PE}{I})\;\theta=-w^2 \theta$
$w^2=\large\frac{P E}{I}$
$T=2 \pi \sqrt{\large\frac{I}{PE}}\;.$

 

answered Feb 12, 2014 by yamini.v
edited Aug 14, 2014 by thagee.vedartham
 

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