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

by superstrings
Tags: acting, charged, force, method, particle, rungekutta
 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?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,706 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
 P: 678 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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