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

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(1) √(2qE)/(md). For a small angular displacement θ from the aligned position, the restoring torque is τ=-pE sin θ≈-pEθ, with p=qd. The dipole rotates about its centre of mass, which is the midpoint, so each charge is at d/2 and I=2m(d/2)²=(md²)/2. Iθ=-pEθ gives ω²=(pE)/I=(qdE)/(md²/2)=(2qE)/(md). ω=√(2qE)/(md).

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

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