Question

A particle of ass m and charge Q is placed in an electric field E which varies with time t ass 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 $\frac{Q{E}_0}{m{\omega }^2}$

Due to verifying electric field, it experiences an verifying force :-

$F=QE=Q{E}_{0}sin\omega t$

at maximum amplitude A, it experience a maximum force of :-

$F_{max}=Q{E}_0$

also, Restoring force in SHM is given by :- $F=m{\omega }^{2}x$

for amplitude , x=A OR,

$m{\omega }^{2}A=Q{E}_0$

$\Rightarrow A=\frac{Q{E}_0}{m{\omega }^2}\to Reqd$