Charged particle final position equation

Hello all,

I am new to PF; this is my first post. I am currently taking a physics class on electricity and magnetism.

I am trying to find an equation to calculate the final position of a charged particle p, given that there are n other particles.

Known:
+ initial (positions and velocities) and charges of all particles (including particle p)
+ mass of particle p
+ final time t

Find:
+ exact final position of particle p after the given time t

I tried working it out on paper, but I got stuck and don't know how to simplify it.
Does anyone know the equation for this?

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berkeman
Mentor
Hello all,

I am new to PF; this is my first post. I am currently taking a physics class on electricity and magnetism.

I am trying to find an equation to calculate the final position of a charged particle p, given that there are n other particles.

Known:
+ initial (positions and velocities) and charges of all particles (including particle p)
+ mass of particle p
+ final time t

Find:
+ exact final position of particle p after the given time t

I tried working it out on paper, but I got stuck and don't know how to simplify it.
Does anyone know the equation for this?
Welcome to the PF.

Initially this sounds like an extremely complicated problem. Can you post the exact problem? Maybe upload a scan of it?

If the particles are all free to move, the motions will be very complex...

I'm not sure why the mods moved this post to homework questions. To clarify, this is not a homework question.

I attached my work and diagram of the system.

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berkeman
Mentor
I'm not sure why the mods moved this post to homework questions. To clarify, this is not a homework question.

I attached my work and diagram of the system.
You are in school, this is a schoolwork question. All such questions go in the Homework Help forums -- that is in the PF Rules that you agreed to when you joined here.

How do your equations simplify for the case where there are 2 particles? Are you really supposed to solve the equations for an arbitrary number of particles and arbitrary starting positions?

Are you really supposed to solve the equations for an arbitrary number of particles and arbitrary starting positions?
Yes, all particles and their positions are arbitrary. It might help you to know that I plan on creating a 2D particle simulator.

It's probably difficult to read my work, but I said that n is the number of particles, so n=2 in my equation when there are two particles.

Last edited:
Borek
Mentor
Sounds like you are trying to solve n-body problem, just with Coulomb forces instead of gravity.

At least as long as you decide to ignore fact moving charges create magnetic fields and another fact that in particle world quantum effects sooner or later kick in.

what quantum effects Borek?

Borek
Mentor
It is not clear what the OP means by "particles". To some extent original description of the problem is not much different from what someone could try to do to describe an atom using classical physics - set of particles being nucleus and electrons. We know this approach won't work, and we have tested and tried methods for solving such systems, using Schroedinger's equation.