The Uniform Field Between Parallel Plates

A single point charge makes a field that weakens with distance and spreads out in curved lines. A flat charged sheet is different: every point on it contributes, and the sideways components from all those contributions cancel out, leaving a field that points straight out from the sheet with the same strength no matter how far you are from it. Put two sheets close together with opposite charges, one positive and one negative, and their fields add up in the gap between them. Outside the gap the two fields cancel almost completely. Inside, you get one field, pointing from positive to negative, the same strength at every point. That is the uniform field.

The strength of that field connects directly to the voltage across the plates: E = V/d, where V is the potential difference and d is the plate separation. Double the voltage and the field doubles. Squeeze the plates closer together and the field gets stronger for the same voltage, because the same energy drop happens over a shorter distance. For plates 120 V apart with a 0.004 m gap, E = 120/0.004 = 30000 V/m.

Fire a charged particle, say an electron, sideways into that gap, moving parallel to the plates. The field pushes it perpendicular to its original motion with constant force, so it accelerates steadily in that direction while cruising at constant speed in the original direction. Split the motion into those two independent directions and the path traced out is a parabola, the same shape you get when gravity pulls a thrown ball downward while it coasts forward. The math is identical: one direction constant velocity, the other constant acceleration from a steady force.