Electron between charged plates

[Melawrghk]

Homework Statement

An electron enters the area between two charged plates having a horizontal speed of 1.9E6. The space between plates is 1cm and the electron enters half way down from the top plate. The length of the plates is 2cm. Find the speed of the electron as it exists the space between plates barely missing the top plate.

The Attempt at a Solution

I figured it would be just an energy question, so I found the initial kinetic energy and the potential energy it would gain through the climb.

As a result though, the speed still stayed the same. I'm not sure if I'm thinking correctly?... Thanks in advance.

 

[AEM]

Seems to me that that when the electron leaves the plates is has a component of velocity in the x- direction and an acquired component of velocity in the y-direction. the magnitude of it's velocity is now larger than when it entered.This problem has a close similarity to a projectile motion problem. If I were solving it, I'd use that analogy.

 

[Melawrghk]

Thanks! I used two basic dynamics formulas for acceleration and distance and I got it! :)

It increased to 2.12E6, apparently.

 

[ps123]

Can you explain which equations you used and how?
I have the same problem.
Thanks in advance.:)

 

[Melawrghk]

Yeah, for sure. Well you know that the electron enters 0.5cm from the top (halfway between the plates) and exists at the top's level. So it had to vertically travel 0.5cm. Since originally it only had an x-component (and this speed remains the same), it had to have some force acting on it 'causing acceleration.

First, I set out to find the time it took for the "journey". I took the length of the plate (2cm, in my case) and divided it by the horizontal speed. This yielded some time, let's call it "t".

Now, from mechanics, there is a formula:
d=(1/2)*a*t^2 and I used that to find the vertical acceleration (0.5cm, t=t).

Next you really have a few ways of doing this. The simplest is:
a=(delta)v/(delta)t = (vf-vi)/t
In that equatoin you know a and t, and you know that vi=0 (initial vertical speed). This equation will give you the vertical speed as the electron exists the space between plates.

Now use Pythagorean Theorem to find the net speed/velocity.

Hope this helped :)

 

[ps123]

Thank you so much! This helped me a lot!
You are excellent at explaining what you did!

Thanks again :)