# Homework Help: Uniform Vertical Force of Electrons, Using Momentum Principle

1. Jan 26, 2010

### leejqs

1. The problem statement, all variables and given/known data
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 , 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).
[IMAGE in attachment]
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?)
(Enter your response in terms of the variables mentioned in the problem. Use "v0" to represent v0.)

2. Relevant equations
position=initial position + average velocity*time
change in momentum (p)= Forcenet*time

3. The attempt at a solution
Well, since this is a conceptual question, only using the variables given, and no quantities, I decided to work backwards...

I know that the yfinal position = the yinitial position + Vavg,y*time.

I believe that since the initial velocity of the electron has only an x component, the y component force just changes the direction of this initial velocity, and not the magnitude. So when making a triangle, as seen in the attached image, the hypotenus=the initial velocity, the opposite side= the distancey, but I can't find the x and y components of the velocity because I don't have a quantity for force, nor an angle to work with.. I'm stuck here. Any help or guidance would be greatly appreciated! Thanks!

http://img704.imageshack.us/img704/255/crtdeflection.png [Broken]

Last edited by a moderator: May 4, 2017
2. Jan 26, 2010

### Gear300

The displacement of the electron along the direction of the acceleration due to the force could be modeled as del(y) = .5*a*t2 + vi*t, in which del() refers to delta/change in, a is the acceleration, t is time, and vi is the initial velocity in the direction of the acceleration; this displacement occurs so long as the electron is within the electric field (after it exits, you can consider the acceleration negligible). You also need the time, which you can find using the horizontal displacement and initial horizontal velocity v0.

3. Jan 26, 2010

### leejqs

would time t = the distance d divided by the initial x velocity, or the the distance L divided by the initial x velocity?