Final answer:
To find the point where an electron and proton pass each other between two parallel plates, calculate the electric field, then apply Newton's second law to find each particle's acceleration and distance traveled before they meet.
Step-by-step explanation:
Distance Where an Electron and Proton Pass Each Other Between Parallel Plates
The problem involves an electron and a proton released simultaneously from rest, but from opposite plates. To find the point at which they pass each other, we apply Newton's second law and the concept of electric force on a charge.
Firstly, we consider the electric field (E) between the plates, which is uniform and can be calculated using the formula E = σ/ε_0, where σ is the surface charge density and ε_0 is the vacuum permittivity. Both the proton and the electron will accelerate in the field, but in opposite directions due to their opposite charges.
The force acting on each particle is given by F = qE, where q is the charge of the particle. Using the formula a = F/m, where a is the acceleration and m is the mass, we can calculate the accelerations, which will be different due to the different masses of the electron and the proton.
Since both particles are released from rest, their velocities as a function of time will be given by v = at, and the distance they travel by d = (1/2)at^2. Setting these distances equal to each other, due to meeting at the same point at the same time, and solving for the distance from the negative plate will give us the point at which they pass each other.