First slide

Electric dipole

Question

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

Moderate

A

${(\frac{pE}{I})}^{1 / 2}$
B

${(\frac{pE}{I})}^{3 / 2}$
C

${(\frac{I}{pE})}^{1 / 2}$
D

${(\frac{p}{IE})}^{1 / 2}$

Solution

When dipole is given a small angular displacement $θ$ about its equilibrium position, the restoring torque will be
$τ = - pEsinθ = - pEθ (as sinθ = θ) or I \frac{d^{2} θ}{{dt}^{2}} = - pEθ (as τ = Iα = I \frac{d^{2} θ}{{dt}^{2}}) or \frac{d^{2} θ}{{dt}^{2}} = - ω^{2} θ with ω^{2} = \frac{pE}{I} \Rightarrow ω = \sqrt{\frac{pE}{I}}$

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