Displacement and Momentum, particle in cathode ray tube with variables

[physics1311]

Homework Statement

In a cathode ray tube (CRT) used in older television sets and oscilloscopes, a beam of electrons is steered to different placed on a phosphor screen, which glows at locations hit by electrons. The CRT is evacuated, so there are few gas molecules present for the electrons to collide with. Electric forces are used to accelerate electrons of mass m to a speed v0 << c, after which they pass between positively and negatively charged metal plates which deflect the electron in the vertical direction (upward in the diagram, or downward if the sign of the charges on the plates is reversed).
CRT deflection
While an electron is between the plates, it experiences a uniform vertical force F, but when the electron is outside the plates there is negligible force on it. The gravitational force on the electron is also negligibly small in this situation. The length of the metal plates is d, and the phosphor screen is a distance L from the metal plates. Where does the electron hit the screen? (That is, what is yf?)

Homework Equations

displacement=V(avg)Δt
Δp=FnetΔt

The Attempt at a Solution

Using the displacement equation over L
L=(v0+v0)/2*Δt rearanged Δt=L/v0
I substituted this Δt into Yf=(v-final+v-initial)/2*Δt
V(fina)l should be the same as v(initial) over L because there are no other forces as states, right?, so we have Yf=v(final)*L/v0

then to find vf I used the momentum principle assumng v(initial)=0
m*v(final)=FΔt (different Δt here)
and to find this Δt i used the displacement equation for x over d,
d=v0/2*Δt
My final answer, which was wrong, was 2*F*d*L/((v0)^2*m

 

[Keith Gellar]

Hope the attached outline helps.

The only difference I can see is that I didn't apply the force over the length from ray gun to screen. The force is only applied while between the plates.

 

[gneill]

Hi Keith G.,

If you're keen to pursue this problem and work out the full solution, here's a diagram you might be able to make use of:

$\Delta y$ is what is sought.

 

[sophiecentaur]

but when the electron is outside the plates there is negligible force on it.

The diagram in post #3 is af an oscilloscope with electrostatic deflection. Afair, the screen is at a positive potential of tens of kV so the electrons ar accelerating towards it once they pass the deflection plates. (I'd expect a longitudinal force which would(?) result in a parabolic trajectory The enhanced kinetic energy of the electrons makes the phosphor bright and increases the deflection on the screen and enhances the sensitivity.

TV display CRTs use magnetic deflection which allows greater deflection angles and the raster display (linear resulting deflection with straight lines etc) is the same for every frame. An oscilloscope would not be suited to magnetic deflection because the deflection you need varies according to the deflection signals.