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Runge-kutta method for a force acting upon a charged particle

by superstrings
Tags: acting, charged, force, method, particle, rungekutta
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superstrings
#1
Nov14-12, 11:21 PM
P: 2
I have this project that involves the runge-kutta method, and I honestly have no clue what I am doing.

I never learned about this before, and I don't know much about ordinary differential equations. I am learning all of this next semester but it is required information for this project.

In my project, I have to model the movement of a test charge through an electric field and program it onto fortran 90.

I know that the Lorentz equation is F=q(E+vxB), and also F=ma (as a special case), and I can equate the two to find acceleration.

I have no idea how I would set this up as an ODE and then use the runge-kutta method. I need to do this so that I can plot a position vs. time graph of the test charge.

Can someone please help me out?
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HallsofIvy
#2
Nov15-12, 07:53 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,310
You have to use "Runge-Kutta" and you have no idea what that means? You need a lot more help than we can give in a few sentences!

Try these:
http://www.myphysicslab.com/runge_kutta.html
http://mathworld.wolfram.com/Runge-KuttaMethod.html
pasmith
#3
Nov30-12, 08:59 AM
HW Helper
Thanks
P: 943
Acceleration is the second derivative of position (x) with respect to time.
The first derivative is velocity (v). It follows that acceleration is the derivative of velocity.

Thus, as a first order ODE, F = ma becomes
[tex]
\frac {dv}{dt} = F(x,v)/m = (q/m)(E + v \times B) \\
\frac{dx}{dt} = v
[/tex]

At this point you can use Runge-Kutta.


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