A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E₁ = E₀x. If another electric field E₂ = 2E₀(y + z) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)? (a) 73% (b) 63% (c) 83% (d) 53%

Answer: (a). For small oscillations ω = √(pE/I), so f ∝ √(E). New field E = E₀ x + 2E₀ y + 2E₀ z, | E| = E₀√(1 + 4 + 4) = 3E₀. f'/f = √(3) ≈ 1.73 Change ≈ 73%, so the answer is (a).

A rigid dipole undergoes a simple harmonic motion about its centre in… | JEE Main 2026 (4 Apr, Shift 2)

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Electric Dipole

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\vec{E}_1 = E_0\hat{x}$ . If another electric field $\vec{E}_2 = 2E_0(\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

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Answer: (a)

For small oscillations $\omega = \sqrt{\frac{pE}{I}}$ , so $f \propto \sqrt{E}$ .
New field $\vec E = E_0\hat x + 2E_0\hat y + 2E_0\hat z$ , $|\vec E| = E_0\sqrt{1 + 4 + 4} = 3E_0$ .
$\frac{f'}{f} = \sqrt{3} \approx 1.73$
Change $\approx 73\%$ , so the answer is (a).

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