Charged Particle Fired between Parallel Plates
By varying several parameters, we can determine the trajectory of a charged particle fired between two parallel plates with a potential difference.
The electric field between two plates is determined by the potential difference and the separation between the two plates : . The acceleration of a particle between the plates is proportional to the magnitude of the electric field. A positively charged particle moves toward the negative plate, a negatively charged toward the positive. You can vary the controls to change the distance the particle travels before hitting a plate.
Assuming that the particle starts at the origin at time with an initial horizontal velocity , the equations of motion are given by
, , so that . Eliminating between the two equations, we can write .
The particle hits a plate when , corresponding to . Solving for , we find
where is the initial horizontal velocity, is the distance between the plates, is the mass of the particle, is the voltage between the plates and is the charge of the particle.
Snapshot 1: with the minimum settings, it is possible to make the particle hit the plate after only .01 m
Snapshot 2: on the other hand, you can set the controls so that the particle travels nearly 16 m
Snapshot 3: when the charge on the particle is reversed in sign, the particle follows a reflected path to the opposite plate