Question

A particle of mass $m$ and charge $Q$ is placed in an electric field of intensity $E,$ which varies with time $t$ as $E=E_0\sin \omega t.$ It will undergo simple harmonic motion of amplitude

• A. $\frac{Q{E}_0^2}{m{\omega }^2}$
• B. $\frac{Q{E}_0}{m{\omega }^2}$
• C. $\sqrt{\frac{Q{E}_0}{m{\omega }^2}}$
• D. $\frac{Q{E}_0}{m\omega }$

Answer 1

The correct option is B $\frac{Q{E}_0}{m{\omega }^2}$

Force on charge $=QE=Q{E}_0\sin \omega t$
acceleration $=\frac{Q{E}_0}{m}\sin \omega t...\left(1\right)$
magnituide of acceleration of particle in SHM is $a=|A{\omega }^2\sin \omega t|...\left(2\right)$
compare equation (1) and (2)
$A{\omega }^2=\frac{Q{E}_0}{m}\Rightarrow A=\frac{Q{E}_0}{m{\omega }^2}$.