A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass ‘m’ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ‘l’. If the dipole is placed in a uniform electric field ‘ $\vec{E}$ ’; such a way that dipole axis makes a very small angle with the electric field, ‘ $\vec{E}$ ’. The angular frequency of the oscillations of the dipole when released is given by:
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Question

A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass ‘m’ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ‘l’. If the dipole is placed in a uniform electric field ‘ $\vec{E}$ ’; such a way that dipole axis makes a very small angle with the electric field, ‘ $\vec{E}$ ’. The angular frequency of the oscillations of the dipole when released is given by:

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G1 Physics · Accepted Answer

Step 1: Use 𝐩 = Σqᵢ𝐫ᵢ (for net zero charge), V = [1/(4πε₀)](𝐩·𝐞ᵣ/r²) and 𝛕 = 𝐩×𝐄 as needed. Step 2: Resolve 𝐩 into components and use the small-angle approximation τ ≈ -pEθ for oscillations. Step 3: Substitute the given geometry and simplify. Final: Option C.