Question

A particle of mass $9\times {10}^{-31}kg$ and charge $-1.6\times {10}^{-19}C$ is projected horizontally with a velocity of ${10}^{5}m/s$ into a region between two infinite, horizontal parallel plates of metal. The distance between the plates is $0.3cm$ and the particle enters $0.1cm$ below the top plate. The top and the bottom plates are connected, respectively, to the positive and negative terminals of $30-$volt battery. Find the components of the velocity of the particle just before it hits one of the plates

• A. $V_x={10}^{5}m/s$
• B. $V_y=1.89\times {10}^{5}m/s$
• C. $V_x=0m/s$
• D. $V_y={10}^{5}m/s$

Answer 1

Answer: (A), (B)

The correct options are
A $V_x={10}^{5}m/s$
B $V_y=1.89\times {10}^{5}m/s$

The particle will hit the upper plate because of attraction

Electric field $=\frac{V}{d}$

where d is the distance between the plates,

Electric field $=\frac{30}{0.3\times {10}^{-2}}=10000V/m$
Upward acceleration $=\frac{force}{mass}=\frac{eE}{m}=\frac{1.6\times {10}^{-19}\times 10000}{9\times {10}^{-31}}=1.78\times {10}^{15}m/s^2$
Take the initial direction of the particle as the x-axis and field direction as the y-axis. From, $v^2-v_0^2=2$as,
$v_y^2=2\times 1.78\times {10}^{15}\times (0.1\times {10}^{-2})$
$v_y=1.89\times {10}^{6}m/s$
The initial velocity along the x-axis remains unchanged as there is no acceleration along the direction.
$\therefore v_y=1.89\times {10}^{6}m/s$ and $v_x={10}^{5}m/s$