Electron Trajectory: Stuck on a difficult problem....

[MiguelBBeats]

Homework Statement

In the oscilloscope shown in Figure 6, an electron
beam is deflected by an electric force produced by
charged metal plates AD and BC. In the region ABCD,

each electron experiences a uniform downward elec-
tric force of 3.20 1015 N. Each electron enters the

electric field along the illustrated axis, halfway
between A and B, with a velocity of 2.25 107 m/s parallel to the plates. The electric force is zero outside
ABCD. The mass of an electron is 9.11 1031 kg.
The gravitational force can be neglected during the

short time interval an electron travels to the fluores-
cent screen, S. Determine how far an electron is below

the axis of entry when it hits the screen.

Relevant Equations

Fbd diagram, fnet = ma, fg = mg

I am very confused on how to go about with this question. The only thing I've tried so far is drawing the fbd of the electron and because of the plates the force applied would cancel which makes it centered between the two plates. As of now that is the only thing I understand, I am not sure how it moves through the screen or how its suppose to be under the axis (axis on the diagram).

 

[PeroK]

You're given the force on the electron in the problem statement. And the mass of the electron. And the initial horizontal speed of the electron.

Can you draw a diagram of the (approximate) trajectory of the electron?

 

[PeroK]

 

[Steve4Physics]

Hi @MiguelBBeats. Welcome from me too! Here are a few things to think about...

each electron experiences a uniform downward electric force of 3.20 1015 N

That's a very big force! (And could be written using the superscript button at the top of the text area as 3.20x10¹⁵N.) Maybe you should check your value is correct!

The mass of an electron is 9.11 1031 kg.

Oh no it isn't!

Relevant Equations:: Fbd diagram, fnet = ma, fg = mg

You are told the gravitational force is negligible. So you can pretend it is zero. That means "fg = mg" is not a relevant equation!

and because of the plates the force applied would cancel which makes it centered between the two plates.

How can the force applied cancel, if it is the only force?

Each electron enters the space between the plates midway between A and B (on the dotted line). But that does not mean the electrons stay on the dottted line!

One plate is positive and the other is negative (can you work out which is which?) and that is the reason there is a constant force on each electron while it is between the plates. (Editted.)

Are you familiar with projectile problems, where the projectile's velocity is initially horizontal? Assuming the answer is 'yes', do you see the relevance?

 

[haruspex]

each electron experiences a uniform downward elec-
tric force of 3.20 1015 N.

Each electron enters the electric field along the illustrated axis, halfway
between A and B, with a velocity of 2.25 107 m/s parallel to the plates.

The mass of an electron is 9.11 1031 kg.

Presumably those are supposed to be
$3.20\times 10^{-15} N$
$2.25 \times10^{7} m/s$ or $2.25\times 10^{-7} m/s$ (which?)
$9.11\times 10^{-31} kg$

not sure how it moves through the screen or how its suppose to be under the axis

You have an object moving horizontally, initially, and subject to a constant downward force. Remind you of anything?
In case there is any misunderstanding, axis referred to is the dashed blue line it starts on.