[Coda]

Well, think about it. If you're an electron, then the closer you get to the positive plate, the harder it'll push you away, but as you get farther away from it you're also getting closer to the negative plate, so it starts pulling harder to pull you towards it. The forces balance out in a way that can be modeled as uniform field strength. (In reality, it's never perfect, especially near the edges.)

The customary variable for charge is q.

Charge is basically just the electromagnetic analogue of mass. It's just a property that matter has that influences how strongly fields act on it, just like more mass means more gravitational force. It measures the imbalance between protons and electrons, but since we're not dealing with individual ions here we've got a unit for macroscopic charges called the coulomb instead of counting electrons. (After all, you don't count the protons and neutrons in a macroscopic object to determine its mass.)