# Electron being shot between two plates

1. Mar 9, 2014

### hvthvt

1. The problem statement, all variables and given/known data

In the figure, a uniform, upward-pointing electric field E of magnitude 2.00×103 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 4 cm and separation d. Electrons are shot between the plates from the left edge of the lower plate.
The first electron has the initial velocity v0, which makes an angle θ=45° with the lower plate and has a magnitude of 5.86×106 m/s. Suppose the distance d between the plates is large enough so that the electron doesn't hit the upper plate. Determine how far horizontally from the left edge on the lower plate the electron will strike.

2. Relevant equations

v[initial, y]^2 + (2*a*deltaY) = 0
acceleration = [eE]/[m]
v[initial,y] + (a*t) = 0

3. The attempt at a solution

I do know how to solve this problem when it actually hits the upper plate, but my problem is: how to deal with the fact that it DOESNT hit it? I know that vx is zero when Xmax is reached. I know that the acceleration is 3.5*10^14 m/s^2
Can anybody help me?

2. Mar 9, 2014

### Andrew Mason

Do you see a similarity between this and projectile motion where the downward force is a uniform gravitational force? Can you use the formula relating launch angle, speed and horizontal range for projectile motion for this problem?

AM

3. Mar 9, 2014

### hvthvt

I guess that is the accelerated motion along the x-axis:

Vox= Vo * cos45 and x=Vox*t
However, I do not know the time it takes. From ma= eE + mg I am able to calculate the acceleration.
I can calculate Ymax by stating that Vy=0 when the particle reaches its maximum distance.
And we know that Vy = Voy - at so Voy= at. This would give me the time that is needed. Calculating this would give me 1.46*10^-8 s. Is this correct?
Can i then just plug it in for x=Vox*t= 0.061 m. ?

4. Mar 9, 2014

### Andrew Mason

I was thinking of R = v02sin2θ/g

See: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra4

How would you adapt this for the electric field in this problem?

AM