Question

A particle having charge $q$ and mass $m$ is projected with velocity $\vec{v}=2 \hat{i}-3 \hat{j}$ in uniform electric field $\vec{E}=E_0 \cdot \hat{j}$. Change in momentum $|\Delta \vec{p}|$ during any time interval $t$ is given by:

• A. $\sqrt{13} M$
• B. $q E_0 t$
• C. $\frac{q E_0 t}{m}$
• D. zero

Answer 1

Answer: (B)

The product of force and time interval is called impulse. Also from Newton's second law, we have
$\vec{F}=m \vec{a}=m \frac{\Delta \vec{v}}{\Delta t}$
$ \vec{F} \cdot \Delta t=m \Delta \vec{v}=\Delta \vec{p}$
The force on charge $q$ due to electric field is $q E_0$
$\therefore \text { Impulse }=q E_0 t .$