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

  1. Nov 14, 2012 #1
    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?
  2. jcsd
  3. Nov 15, 2012 #2


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  4. Nov 30, 2012 #3


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    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
    \frac {dv}{dt} = F(x,v)/m = (q/m)(E + v \times B) \\
    \frac{dx}{dt} = v

    At this point you can use Runge-Kutta.
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