Homework Help: Electron speed

kasse · May 11, 2008

1. The problem statement, all variables and given/known data

The potential between the cathode and the screen of a computer is 12kV. What is the speed of an electron when it reaches the screen if it starts at rest at the cathode?

3. The attempt at a solution

First I found that the force that acts on the electron is 1.922E-15 N. I can then find the acceleration, but I need the distance between the cathode and the screen to find the speed.

Can I use energy conservation? Probably. Gravitational forces can be ignored. (1/2)mv^2 = E_pot But what is the the expression for potential energy? Not mgh. Can I simply replace m with charge, g with E and h with the potential?

1/2)mv^2 = eEU

?

lzkelley · May 11, 2008

Generally the electric and gravitational potentials will NOT take the same form - good try though. The answer is much simpler - it is contained in the problem statement (hint hint: what are the first 2 words?).

kasse · May 11, 2008

The potential. Probably eV then? But why?

Lojzek · May 12, 2008

The idea of replacing mgh with eEh is a bit careless but has some meaning if understood properly: Work done by constant forces is F*s, where F is -mg in the first case and eE in the second case. Since the change of energy equals -work, the analog expression of mgh is actually -eEh. However the electric field is not always uniform, so -Eh must generaly be replaced by Integral(-E*dh)=U

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Homework Help: Electron speed

kasse

lzkelley

kasse

Lojzek