19.1 Motion in Uniform Electric Fields

In a uniform electric field, the electric force on a particle is constant in magnitude and direction as long as the particle stays inside the uniform region. That means acceleration is constant too. For a positive charge, acceleration is along E. For a negative charge, acceleration is opposite E. This is the exact same kinematic structure as constant-acceleration motion in Chapter 1.

If the particle starts from rest, or if initial velocity is exactly parallel to E, the path stays straight. Speed changes because force has a component along velocity. This is the fastest case to solve: one-dimensional constant acceleration with clear sign convention.

When a particle enters the field with horizontal velocity while E is vertical, there is no horizontal force in the ideal model. Horizontal speed stays constant, while vertical velocity changes uniformly. That is mathematically identical to horizontal projectile launch with gravity replaced by qE/m, so the trajectory is parabolic.

This component strategy is also the easiest way to decide whether a particle will strike one plate before exiting. Compute the transit time from plate length and horizontal speed, then evaluate vertical displacement at that time. If displacement magnitude exceeds half-gap, the particle collides with a plate before leaving the field region.

Unlike magnetic force, electric force can do work because it can have a component along displacement. In uniform fields between plates, energy changes are often faster to compute from potential difference than from acceleration-time methods. This provides an independent check on kinematics-based answers.