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

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.

 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.