A stream of positively charged particles having $\dfrac qm=2\times10^{11}\ \text{C kg}^{-1}$ and velocity $\vec v_0=3\times10^7\hat i\ \text{m s}^{-1}$ is deflected by an electric field $1.8\hat j\ \text{kV m}^{-1}$. The electric field exists in a region of $10\ \text{cm}$ along $x$ direction. Due to the electric field, the deflection of the charged particles in the $y$ direction is ______ mm.
Numerical value type. Enter your answer.
Answer: 2
$a_y=\dfrac qmE=2\times10^{11}\times1.8\times10^3=3.6\times10^{14}\ \text{m s}^{-2}$; time in the field $t=\dfrac{0.1}{3\times10^7}=\dfrac13\times10^{-8}\ \text{s}$.
$$y=\frac12a_yt^2=\frac12\times3.6\times10^{14}\times\frac19\times10^{-16}=2\times10^{-3}\ \text{m}=2\ \text{mm}$$
Solution by Sreeraj P, M.Sc Physics