Acceleration of electron due to finite sheet at voltage

[AlexCdeP]

Homework Statement
Suppose I am undertaking an experiment using a scanning electron microscope in which there is a positively charged plate underneath the target sample. I want to find the change in energy of the electron due to a positive voltage on this plate from the point it leaves the electron gun to the point it hits the sample. The only things I know are the voltage on the plate, the distance from the gun to the sample and the dimensions of the plate/sheet.

The attempt at a solution
My main question is can this be solved or do I need more information? At the moment I can only think of a way to do it by measuring the potential gradient above the plate to get the electric field. I know the electric field due to a finite sheet and I know that E = -∇V. Since the electron is directly above the sheet only the gradient in the z-direction(beam direction) has an influence, then once I get the electric field I can solve for the force and find the change in velocity.

I apologise if this is a simple problem, it's been a while since I did electromagnetism.

Thanks in advance.

 

[mfb]

Sounds like a good approach.
If your sample is conductive, you can also try to directly measure (or even influence) its potential.

 

[AlexCdeP]

Thanks, so would you agree until I actually get the system implemented its going to be difficult/impossible to calculate the change in energy? It's frustrating because I feel like there must be a way to calculate the electric field theoretically knowing only the dimensions of the plate and the voltage a the surface of the plate.

Also that's a good point on conductive samples. I'm looking at resistive samples at the moment, polymers specifically, but Ill probably still have to take into account the effects of the sample.

 

[mfb]

Conductivity is only a matter of time and capacitance.

I'm sure there is some way to model the system to evaluate it, but you'll need more details.

 

[AlexCdeP]

Thanks for the reassurance. I'll hopefully get on with implementation and then add an update somewhere when I work out how to model it as I can't find a similar problem online at the moment, although I know that it's been done before.