When a charged particle enters an electric field, it experiences a force proportional to its charge and the electric field strength. This force causes the particle to accelerate according to Newton's second law. Let's examine how a positively charged particle behaves in a uniform electric field between two parallel plates.
The electric force acting on a charged particle is given by F equals q times E, where q is the particle's charge and E is the electric field strength. Using Newton's second law, we can find the acceleration as a equals F over m, which equals q E over m. This shows that the acceleration is directly proportional to the charge and field strength, and inversely proportional to the particle's mass.
Now let's observe the motion of the charged particle. Starting from rest, the particle accelerates due to the constant electric force. The motion follows kinematic equations: velocity equals acceleration times time, displacement equals one half acceleration times time squared, and velocity squared equals two times acceleration times displacement. Watch as the particle moves from the negative plate toward the positive plate.
The electric field performs work on the charged particle as it moves through the field. The work done equals the charge times the electric field strength times the distance traveled. This work is converted into kinetic energy, following the work-energy theorem. Initially at rest, the particle gains kinetic energy equal to one half m v squared, which equals the work done by the electric field.