Question
A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field ${\overrightarrow{E}}_{1} = E_{0}\widehat{x}$. If another electric field ${\overrightarrow{E}}_{2} = 2E_{0}(\widehat{y} + \widehat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate) ?
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Solution
Sol. [Key Concept: Frequency $f \propto \sqrt{E}$; the field magnitude rises $E_{0} \rightarrow 3E_{0}$, so $\%$ change $= (\sqrt{3 - 1)} \times 100 \approx 73$.]
Initial freq. $f_{1} = \frac{1}{2\pi}\sqrt{\frac{P\left( E_{0} \right)}{I}}$
Final $EF = E_{0}\widehat{i} + 2E_{0}(\widehat{j} + \widehat{k})$
Magnitude $= 3E_{0}$
Final Freq. $f_{2} = \frac{1}{2\pi}\sqrt{\frac{P\left( 3E_{0} \right)}{I}}$
$\%$ change $= \frac{\Delta f}{f_{1}} = (\sqrt{3} - 1) \times 180 \simeq 73$
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