Question

A particle, of mass $10^{-3}kg$ and charge $1.0C$, is initially at rest. At time $t=0$, the particle comes under the influence of an electric field $\vec{E}\left(t\right)=E_0$ sin $\omega t\hat{i}$, where $E_0=1.0N{C}^{-1}$ and $\omega =10^{3}rad{s}^{-1}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $m{s}^{-1}$, attained by the particle at subsequent times is _______.

Answer 1

Answer: 2

$n=10^{-3}kgq=1Ct=0$

$E=E_0\sin \omega t$
Force on particle will be $F=qE$
$=q{E}_0\sin \omega t$
At $V_{max}a,F=0$
$q{E}_0\sin \omega t=0$
$F=q{E}_0\sin \omega t$
$\frac{dv}{dt}=q\frac{E_0}{m}\sin \omega t$
$\underset{0}{\overset{v}{\int }}dv=\underset{0}{\overset{\pi /\omega }{\int }}\frac{q{E}_0}{m}\sin \omega tdt$
$V-0=\frac{q{E}_0}{m\omega }[-\cos \omega t{]}_0^{\frac{\pi }{\omega }}$
$V-0=\frac{q{E}_0}{m\omega }[(-\cos \pi )-(-\cos 0)]$
$V=\frac{1\times 1}{10^{-3}10^3}\times 2=$
$2m/s=2.00$