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

pEI1/2

b

pEI3/2

c

IpE1/2

d

pIE1/2

answer is A.

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Detailed Solution

When dipole is given a small angular displacement θ about its equilibrium position, the restoring torque will beτ=−pEsin⁡θ=−pEθ             ( as sin⁡θ≈θ) or  Id2θdt2=−pEθ             as τ=Iα=Id2θdt2or   d2θdt2=−ω2θ with ω2=pEI ⇒ω=pEI
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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