Distance for electron to stop due to charged plane

[kunkle]

Ran into a question in my amateur research. Been waaay too long since college physics, and I've exhausted searches. This is the theoretical question:

Assume a non-conducting, infinite plane charged to +10 kV. An electron leaves perpendicular to the surface with an energy of 10 keV. How far does the electron travel before it is brought to a stop by the attraction to the charged plane? Trying to figure out (at least theoretically), if my electrons are smacking into the chamber walls. Would like to be able to calculate the distance for any voltages used.

Closest thing I've found is this: Question 5
http://www.phys.ufl.edu/~acosta/phy2061/Exams/Exam1_soln_f06.pdf
Very close to what I need, except they use charge density on the plane; I only know the floating voltage of the plane. I think I almost have it, but I don't seem to be able to convert voltage (V) to charge density or electric field (E) in the equations.

Thanks for any help.

 

[haruspex]

Ran into a question in my amateur research. Been waaay too long since college physics, and I've exhausted searches. This is the theoretical question:

Assume a non-conducting, infinite plane charged to +10 kV. An electron leaves perpendicular to the surface with an energy of 10 keV. How far does the electron travel before it is brought to a stop by the attraction to the charged plane? Trying to figure out (at least theoretically), if my electrons are smacking into the chamber walls. Would like to be able to calculate the distance for any voltages used.

Closest thing I've found is this: Question 5
http://www.phys.ufl.edu/~acosta/phy2061/Exams/Exam1_soln_f06.pdf
Very close to what I need, except they use charge density on the plane; I only know the floating voltage of the plane. I think I almost have it, but I don't seem to be able to convert voltage (V) to charge density or electric field (E) in the equations.

Thanks for any help.

Potential is always relative to some arbitrarily defined zero. Normally one would choose the potential at infinity as zero, but that does not work here. An infinite uniformly charged sheet, were such a beast feasible, has a uniform field at all distances, so the difference between the potential of the sheet and that at infinity is infinite. For this reason, one usually selects the sheet itself as the zero potential.
In short, your question is unanswerable because the voltage cannot be assigned a meaning. In particular, it does not tell you the charge density.

 

[kunkle]

Potential is always relative to some arbitrarily defined zero. Normally one would choose the potential at infinity as zero, but that does not work here. An infinite uniformly charged sheet, were such a beast feasible, has a uniform field at all distances, so the difference between the potential of the sheet and that at infinity is infinite. For this reason, one usually selects the sheet itself as the zero potential.
In short, your question is unanswerable because the voltage cannot be assigned a meaning. In particular, it does not tell you the charge density.

I had a bad feeling when none of the equations I had collected would let me substitute V for charge density or E no matter how you slice it. At least I know why now. Thank you.

What if I were to measure the E field strength with an electric field meter? Not that I have one, but that can be fixed. That can be converted to charge density. Does it matter at what distance the E field is measured? I know that's V/m, but that decreases as a square of the distance, right? Measure as close as physically possible to the source?

Of course, the electrode is not actually an infinite plane; but I thought I would get closer to reality than treating it as a point charge. FWIW, it is actually about 6 inches in diameter. Figure as a point charge and an infinite plane, then average the two to get in the ballpark realistically?

 

[Drakkith]

What if I were to measure the E field strength with an electric field meter?

If I remember my E&M class correctly, a charged infinite plane has a perfectly uniform e-field that stays the same strength no matter how far you get from it. Try drawing a slice through the plane and the accompanying field lines and you should see that they are parallel to each other instead of diverging.