A rigid electric dipole performs small angular oscillations about its centre in a uniform electric field E₁ = E₀î. A second field E₂ = 2E₀(ĵ+k̂) is then added. Approximately what is the percentage increase in the oscillation frequency?
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Question

A rigid electric dipole performs small angular oscillations about its centre in a uniform electric field E₁ = E₀î. A second field E₂ = 2E₀(ĵ+k̂) is then added. Approximately what is the percentage increase in the oscillation frequency?

Options

G1 Physics · Accepted Answer

For a dipole undergoing small angular oscillations in a uniform electric field, f = (1 ÷ 2π)√(pE ÷ I), so f ∝ √E. Initially, |E₁| = E₀. After adding E₂: E(final) = E₀î+2E₀ĵ+2E₀k̂. Its magnitude is |E(final)| = E₀√(1²+2²+2²) = 3E₀. Therefore, f₂ ÷ f₁ = √(3E₀ ÷ E₀) = √3. Percentage increase: [(f₂-f₁) ÷ f₁]×100 = (√3-1)×100 ≈ 73.2%. Therefore the approximate increase is 73%. Correct option: A.