An electric dipole of mass m, charge q and length l is placed in a uniform electric field ⃗E=E₀̂i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be

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(3) 2π√(ml)/(2qE₀). Each charge sits at l/2 from the centre, so the moment of inertia about the centre is I=2m(l/2)²=(ml²)/2. Dipole moment p=ql, and for a small angle θ the restoring torque is τ=-pE₀ sin θ≈-qlE₀θ. Iθ=-qlE₀θ⇒ω²=(qlE₀)/(ml²/2)=(2qE₀)/(ml). T=(2π)/ω=2π√(ml)/(2qE₀).

An electric dipole of mass m, charge q and length l is placed in a uniform electric field ⃗E=E₀̂i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be

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