Force on electron passing through Electric Field (calculate)

[Blackhawk4560]

Good afternoon,

I hope this is in the right place... Anyway, diving right in-

Say I have a classic CRT- How do I calculate the energy, in eV, that the electrons have upon reaching the anode? Also, is there a way to derive the speed of the electrons as well? See the attached image to clarify...

I'm trying to put the old TV's CRTs into perspective, so user MFB was already helping me out with that on another thread already, and that just spawned this question...

Thanks in advance!

 

[mfb]

The energy gained is q*V. For an electron, this means 1 V of potential difference leads to 1 eV of energy.

 

[Blackhawk4560]

That was an easier answer than I could dream for! Thanks again mfb!

 

[mfb]

Well, the unit eV was defined for exactly this purpose.

 

[ChrisVer]

Yes you can derive the speeds by using the F=qE.
Or better: the conservation of energy...I think this should give you:

$v = \sqrt{v_0^2 + \frac{2eEd}{m}}$
$d$ : the distance traveled by the electron within the applied force
$E$ : the electric field
$m$: the mass of the electron
$v_0$ : the initial velocity (when entering the field)

 

[ZapperZ]

There is a FAQ covering a similar topic:

https://www.physicsforums.com/threads/energy-gained-by-charge-in-an-electrostatic-field.765723/

Zz.

 

[Blackhawk4560]

You guys are too good!

EDIT: Quick questions, first, for future search ability, what is this formula called? secondly, what does "e" represent? Is that e as in 2.7...? Thaaaaaaank you everyone

 

[mfb]

The elementary charge.

The formula ChrisVer posted? Just energy conservation with nonrelativistic motion.

 

[ChrisVer]

nonrelativistic and nonradiating motion

 

[mfb]

In the nonrelativistic limit the radiation vanishes ;).