Question

An electron is projected with an initial speed 1.00×10^6 m/s into the uniform field between the parallel plates in the figure (Figure 1) . 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 speed of the electron as it emerges from the field?

Answer 1

I don't know how you'd see the figure, but I can try to explain what the figure looks like.

Answer 2

It's basically two plates 1 cm apart and 2 cm in length for the plates. And then there is an electron in between the plates moving to the right Vo.

Answer 3

There is a relationship between forces acting on an electron in motion in an electric field. I am not real familiar with them. I think that there may be some kinetic energy loss because the electron is going upward in a downward projected electric field. You see, the electric field opposes the motion of the electron to slow it down. This may require an integral setup to solve. Let me think a bit. Do you agree with my statements so far?

Answer 4

Yes, completely agree with that

Answer 5

Well, since the force acting downward on the electron is the electron's charge multiplied by the field strength, the downward force acting on the electron may be found. Then it becomes almost like a projectile problem. Do you agree so far?

Answer 6

Yup, agree with that

Answer 7

Okay, I thought of an easy way to solve without an integral. The electron travels in the upward direction half the distance between the plates. So the force acts on the electron for that distance. Force x Distance = Energy lost. The energy lost is the kinetic energy,
0.5mv^2. Once you calculate energy lost, you can solve for the change in kinetic energy. Actually it is FxD = 0.5m(v1^2-v2^2) Where v1 is the initial and v2 the final velocity. That is the setup. The next step is to solve for v2.

Answer 8

How do I know what the force is to solve for energy lost?

Answer 9

That force is the electric field strength multiplied by the charge of an electron.

Answer 10

But all I'm given is the initial speed and distances

Answer 11

Well, the field strength must be known in order to solve this problem. For example, imagine if the field strength is zero. In that case, the velocity would not change at all. So the problem does not give enough information if that field strength is missing.

Answer 12

So, are you saying that it is unsolvable?

Answer 13

Without giving the field strength, yes.
Of course, maybe there is something in the drawing that implies a field strength. Is that a possibility?

Answer 14

I'll try to draw out the drawing on here as best I can

Answer 15

-------------*
l l l l l l l
e*
l l l l l l l
-------------

Traveling left to right * to *. The dashed lines are the plates. And the lines in between are arrows pointing downward

Answer 16

That field is said to be uniform. There is probably some principle or assumption that would enable us to determine the field strength. But it eludes me now.

Answer 17

Anything Algebraic!?

Answer 18

you know Vy and Vx...
find speed :)

Answer 19

Questions?

Answer 20

I got 500,000 for Vy. And how do you solve for Vx?

Answer 21

It's given

Answer 22

Oh, ok. So now, how do I find speed with Vy and Vx?

Answer 23

Is this solution based on a parabolic trajectory, Algebraic?