Analyse the motion of charged particles in the uniform electric field between parallel plates, using field strength, force and energy.

What this dot point is asking

You need to analyse the motion and energy of a charged particle in the uniform field between parallel plates.

The uniform field between parallel plates

Two flat, parallel, oppositely charged plates produce an (almost) uniform electric field in the gap - the field lines are evenly spaced, straight, and run from the positive to the negative plate.

Because the field is uniform, a charge in the gap feels the same force everywhere, so it has constant acceleration - directly analogous to projectile motion under gravity.

Force, acceleration and motion

The force on a charge $q$ in the field is constant:

and the acceleration is $a = F/m = qE/m$. A particle released from rest accelerates uniformly toward the oppositely charged plate, so the constant-acceleration kinematics equations apply.

If a charge enters the field sideways (perpendicular to the field), it follows a parabolic path, exactly like a projectile: constant velocity along the plates, constant acceleration across them. This is the basis of the cathode-ray oscilloscope.

Energy and potential difference

Moving a charge through a potential difference transfers energy.

This gives a direct route to the final speed of an accelerated particle without needing the field or distance.

The electronvolt

Because $W = qV$, an electron moved through 1 volt gains $1.60\times10^{-19} \text{ J}$. This convenient unit is the electronvolt (eV): $1 \text{ eV} = 1.60\times10^{-19} \text{ J}$. It is widely used in atomic and particle physics.