A particle of mass m and charge Q is placed in an electric field E which varies with time t as E = E₀ sin $ω$ t . It will undergo simple harmonic motion of amplitude

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$\frac{{QE}_{0}^{2}}{{mω}^{2}}$

$\sqrt{\frac{{QE}_{0}^{}}{{mω}^{2}}}$

$\frac{{QE}_{0}^{}}{mω}$

$\frac{{QE}_{0}^{}}{{mω}^{2}}$

answer is B.

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Detailed Solution

$E = E_{0} \sin ω t; F = EQ = E_{0} Qsin ω t$

$\Rightarrow a = \frac{E_{0} Q}{m} \sin ω t \Rightarrow a_{max} = \frac{E_{0} Q}{m}$

${Aω}^{2} = \frac{E_{0} Q}{m} \Rightarrow A = \frac{E_{0} Q}{{mω}^{2}}$

$(∵ A is amplitude)$

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