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Q.

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and 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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a

large {left( {frac{{pE}}{I}} right)^{1/2}}

b

large {left( {frac{{pE}}{I}} right)^{3/2}}

c

large {left( {frac{I}{{pE}}} right)^{1/2}}

d

large {left( {frac{p}{{IE}}} right)^{1/2}}

answer is A.

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Detailed Solution

When dipole is given a small angular displacement θ  about it's equilibrium position, the restoring torque will be
large tau = - ,pEsin theta = - ,pEtheta   (as sinθ =θ )
large or Ifrac{{{d^2}theta }}{{d{t^2}}} = - pEtheta   large (as tau = Ialpha = Ifrac{{{d^2}theta }}{{d{t^2}}}

large or frac{{{d^2}theta }}{{d{t^2}}} = - {omega ^2}thetalarge with {omega ^2} = frac{{pE}}{I}  large Rightarrow omega = sqrt {frac{{pE}}{I}}

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