A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field

Question

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 ${\vec{E}}_{2} = 2 E_{0} (\hat{y} + \hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)? [2026]

Smart Achievers · Accepted Answer

(1)

$Initial freq. f_{1} = \frac{1}{2 π} \sqrt{\frac{P (E_{0})}{I}}$

$Final electric field = E_{0} \hat{i} + 2 E_{0} (\hat{j} + \hat{k})$

$Magnitude = 3 E_{0}$

$Final Freq. f_{2} = \frac{1}{2 π} \sqrt{\frac{P (3 E_{0})}{I}}$

$% change = \frac{Δ f}{f_{1}} = (\sqrt{3} - 1) \times 100 ≃ 73$

$\Rightarrow 73 % increases$

Solution

1 73%

2 63%

3 83%

4 53%

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