# Derivation of formula - electrons in an electric field

#### synthesized

I need to derive the following formula, in relation to the angle between the electron beam and the plates where the beam of electrons hits the plates in a Teltron tube:

$$tan \theta = \frac{Eqs_{h}}{mv_{h} ^2}$$

I think I managed to complete about 70% of this, but I need to found out what it is in its entirety!

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#### OlderDan

Homework Helper
synthesized said:
I need to derive the following formula, in relation to the angle between the electron beam and the plates where the beam of electrons hits the plates in a Teltron tube:

$$tan \theta = \frac{Eqs_{h}}{mv_{h} ^2}$$

I think I managed to complete about 70% of this, but I need to found out what it is in its entirety!
I think we need more information here. Define the variables. Are there both electric and magnetic fields involved in this? Is this something like what you have?

http://www.telatomic.com/ttubes4.html [Broken]

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#### synthesized

yeah, that is pretty much the teltron tube i'm referring to. This is only an electric field.

in the eqn:
- theta = the angle between the plates (where the stream of electrons hits) and the electron gun (see attached pic)
- E = size of the electric field between the plates
- q = charge of the electron
- s = the horizontal (x) displacement between the electron gun and where the electron stream hits the plates.
- m = mass of the electron
- v = horizontal velocity of the electrons in the electron stream

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#### OlderDan

Homework Helper
synthesized said:
yeah, that is pretty much the teltron tube i'm referring to. This is only an electric field.

in the eqn:
- theta = the angle between the plates (where the stream of electrons hits) and the electron gun (see attached pic)
- E = size of the electric field between the plates
- q = charge of the electron
- s = the horizontal (x) displacement between the electron gun and where the electron stream hits the plates.
- m = mass of the electron
- v = horizontal velocity of the electrons in the electron stream
Now we can help Given v and s you can calculate the time of flight, t, through the electric field. From E and q you can calculate the force, F, on the charge. From F and m you can calculate the acceleration, a, toward the positive plate. From a and t you can calculate the velocity component, u, perpendicular to the plate at the moment of impact. $$tan \theta$$ is the ratio of the two velocity components, u and v.

#### synthesized

Thanks Dan

"Derivation of formula - electrons in an electric field"

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