# Acceleration of electron due to finite sheet at voltage

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1. Mar 11, 2015

### AlexCdeP

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

2. Mar 11, 2015

### Staff: Mentor

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

3. Mar 11, 2015

### 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.

4. Mar 11, 2015

### Staff: Mentor

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.

5. Mar 11, 2015

### 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.