# An electron is then shot between the plates

1. Sep 9, 2010

### Gizmo44

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 = 2.00 cm. 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. Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates.

2. Relevant equations
I believe that the proper equations that one could use would be the following:

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

3. The attempt at a solution

I had to solve a similar problem like this, where the electron had actually hit one of the metal plates. However, I think that this time it is different and I don't necessarily know where to go from here. I tried to do what I had done for the other part, but the answers yielded incorrect results.

Any help at all is greatly encouraged.

-M

2. Sep 9, 2010

### Delphi51

Welcome to PF, Gizmo!

Well, you need the trajectory of the electron, probably in the form of a nice y = function of time, and x = function of time formula.
First step: separate the initial velocity into horizontal and vertical parts. I would then use d = vt for the horizontal part and
d = Vi*t + .5*a*t² for the vertical part. You would then be in a position to predict the maximum height and see whether it is greater than the 2 cm you have room for.

Last edited: Sep 9, 2010
3. Sep 9, 2010

### seto6

notice that you are given more information... but not directly.. you can find Voltage then..use energy to solve..use the 5 kinematics equation

4. Sep 9, 2010

### rl.bhat

It should be L = v*t

5. Sep 9, 2010

### Delphi51

Explanation needed . . . L is given to be fixed at 4 cm but I'm thinking of a function of time with varying value, hence d = v*t. Actually x = v*t would be clearer but good old d = v*t should bring back memories from high school.

Ah, perhaps you are interested in calculating the time when it reaches the far side of plate region. But we really need the trajectory for the whole flight through that region in order to see if it hits the top plate on the way.