First slide

Electric dipole

Question

An electric dipole is situated in an electric field of uniform intensity E/4 whose dipole moment is 2p 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

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

Solution

When dipole is given a small angular displacement $θ$ about it's equilibrium position, the restoring torque will be
$τ = - 2 p \frac{E}{4} \sin θ = - \frac{p E}{2} θ$
$(a s \sin θ = θ)$
$I \frac{d^{2} θ}{d t^{2}} = - \frac{p E}{2} θ$ $(a s τ = I α = I \frac{d^{2} θ}{d t^{2}})$
$o r \frac{d^{2} θ}{d t^{2}} = - ω^{2} w i t h ω^{2} = \frac{p E}{2 I} \Rightarrow ω = \sqrt{\frac{p E}{2 I}}$

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