First slide

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

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

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

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

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

Solution

When dipole is given a small angular displacement $θ$ about its equilibrium position, the restoring torque will be
$τ = - p E \sin θ = - p E θ (as \sin θ \approx θ)$
$or I \frac{d^{2} θ}{d t^{2}} = - p E θ (as τ = I α = I \frac{d^{2} θ}{d t^{2}})$
$o r \frac{d^{2} θ}{d t^{2}} = - ω^{2} θ with ω^{2} = \frac{p E}{I} \Rightarrow ω = \sqrt{\frac{p E}{I}}$

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