Question

A particle of mass $m$ and charge $q$ is placed in an electric field $E$ which varies with time $t$ as $E=E_o\sin \omega t$. It will undergo SHM of amplitude

• A. $\frac{Q{E_o}^2}{m{\omega }^2}$
• B. $\frac{Q{E}_o}{m{\omega }^2}$
• C. $\sqrt{\frac{Q{E_o}^2}{m{\omega }^2}}$
• D. $\frac{Q{E}_o}{m\omega }$

Answer 1

The correct option is A $\frac{Q{E_o}^2}{m{\omega }^2}$

$F=QE=Q{E}_o\sin \omega t$

$⟹F_{max}=Q{E}_o$

And, we know that maximum force is given by $m{\omega }^{2}A.$

$⟹m{\omega }^{2}A=Q{E}_o$

$⟹A=\frac{Q{E}_o}{m{\omega }^2}$

Answer-(B)