# Electron in an Electric Field

1. Jan 25, 2009

### CEJ__

1. The problem statement, all variables and given/known data
An electron is projected with an initial speed v0 = 1.60 x 10^6 m/s into a uniform field between two parallel plates. Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.

The question gives a diagram which I'll try to reproduce here.

----------- *
| | | | |
e*
| | | | |
-----------

So in this diagram, the top and bottom lines are the plates. e is the electron, and the | are the field lines. The field lines flow from top to bottom. The two *'s are to show the start and end points of the electron--it travels on a parabolic path from the left * to the right *.
The distance between the two plates is 1.00cm, and the length of the plates is 2.00cm.

2. Relevant equations
The version of the electric field equation that we are using is E = (1/4*pi*k)*q / r^2 where (1/4*pi*k) = 9E9 N*m^2/C^2

3. The attempt at a solution

I thought perhaps we could take the integral of the electric field equation to sum up all the little dr values as the electron travels, but as it starts at .5cm and ends at 0, this gives a rather nasty 1/0 term. There are other parts to the problem, so some of the information might not be useful. Does anyone have any pointers for how to go about this?

-CEJ