- Home
- Standard 12
- Physics
A particle, of mass $10^{-3} kg$ and charge $1.0 C$, is initially at rest. At time $t =0$, the particle comes under the influence of an electric field $\dot{E}( t )= E _0 \sin \omega t \hat{ i }$, where $E _0=1.0 N C ^{-1}$ 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. . . . . .
$2$
$5$
$8$
$9$
Solution
Velocity is maximum when acceleration is zero.
$F =0$
$E = E _0 \sin \omega t =0$
$\sin \omega t =0$
$\omega t =0 \text { or } \pi$
$t =\frac{\pi}{\omega}$
$E = E _0 \sin \omega t$
$F = qE = qE 0 \sin \omega t$
$a =\frac{ qE }{ m }=\frac{ qE }{ m } \sin \omega t$
$a =\frac{ dv }{ dt }=\frac{ qE _0}{ m } \sin \omega t$
$\int_0^v d v=\frac{q E_0}{ m } \int_0^{ t } \sin \omega t$
replacing $t =\frac{\pi}{\omega}$
$v =\frac{2 qE _0}{\omega m }$
$v _{\max }=\frac{2 \times 1 \times 1}{10^3 \times 10^{-3}}=2$
