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Rungekutta method for a force acting upon a charged particle 
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#1
Nov1412, 11:21 PM

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I have this project that involves the rungekutta 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 rungekutta 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? 


#2
Nov1512, 07:53 AM

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P: 39,339

You have to use "RungeKutta" 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/RungeKuttaMethod.html 


#3
Nov3012, 08:59 AM

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P: 945

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 RungeKutta. 


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