I am designing a simple electrostatic simulator see attached diagram, the blue line is the nozzle and the red piece is the electron emitter.
I suppose that the charges will be distributed with the same surface density in the blue line as long it is at the same potential.
The first question is:
What is the simplest way to calculate the charge?
If it is considered as a capacitor, Q=CV, where C is the capacity of the “capacitor” that I have made, but I do not know if it right as long as the plates have finite dimensions and the distance between them is different.
The second question is where to set the ground, because the field would be different. Does it depend on the electrode area?
At the end I measured the electric field with result that the overall charge is the same in both pieces so the charge density account inverse to the surface.
As expected the electric field fall with the inverse of the distance
Here are the test report. I had to modify the classical equation adding a constant to fit with test data at short range
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