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Question:

An electric dipole is formed by two equal and opposite charges q with separation d. The charges have the same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is:-

qE2md

qEmd2

2qEmd

qEmd

Solution:

Correct option is C. 2qEmd

Moment of inertia (I) = m(d/2)² × 2 = md²/2

Now by τ = Iα
(qE)(d sin θ) = md²/2 α
α = (2qE/md) sin θ

For small θ ⇒ α = (2qE/md) θ

⇒ Angular frequency ω = √(2qE/md)