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

1. Nov 14, 2012

### superstrings

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.

2. Nov 15, 2012

### HallsofIvy

Staff Emeritus
3. Nov 30, 2012

### pasmith

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.