Charged Particle in a Uniform Electric Field. Calculate the vertical distance from the center line from where the particle will exit the parallel plate region.

 

Charged Particle in a Uniform Electric Field

Calculate the vertical distance from the center line 

from where the particle will exit the parallel plate region.

Concepts: Projectile motion concepts, treat x and y axis as two different motions, no one pulling it from the x-axis so $a_x=0$, initial velocity only in x-direction so $u_y=0$.

Note that the grid square shown in the figure has a distance of 1 cm, so the x and y distances can be measured as required.

X-axis Displacement

\[S_x=u_x t+\frac{1}{2}a_x t^2\]

\[10\hspace{2mm} cm = 10^6 t + 0\]

\[10^{-7}\hspace{2mm} s = t \]

Y-axis Displacement

\[S_y=u_y t+\frac{1}{2}a_y t^2\]

\[=0+\frac{1}{2}\left(3.5\times 10^{12}\right)\times\left(10^{-7}\right)^{2}\]

\[=1.7\times10^{-2}\hspace{2mm} m\]

\[=1.7\hspace{2mm} cm\]

$a_y$ Acceleration in Y-direction

\[F_y=qE=m a_y\]

\[a_y=\frac{qE}{m}\]

\[=3.5\times10^{12}\hspace{2mm} m/s^2\]

1.7 cm matches with the figure shown.