Calculating Electron Speed at 12kV Potential Difference on a Computer Screen

[kasse]

Homework Statement

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?

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]

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]

The potential. Probably eV then? But why?

 

[Lojzek]

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