What are some methods for plotting the path of a particle in a magnetic bottle?

[foxjwill]

I was wondering about a good application to plot the path of a particle in a magnetic bottle (i.e. the magnetic field in the region between two coaxial circular loops of wire)

I was thinking that maybe I could use Biot Savert's (sp.) law

$$d\textbf{B} = \frac{\mu_0}{4\pi} \frac{Id\textbf{l} \times \textbf{\hat{r}}}{r^2}$$

and

$$d\textbf{F} = q\textbf{v} \times d\textbf{B}$$

but, as I mentioned earlier, I don't have a good application for that. Worse comes the worse, I could try and write a program to do it, but

1. I don't know what method of approximation to use, and
2. I'm not very good at coding.

 

[lzkelley]

Thats a surprisingly complex situation; you won't be able to plot it analytically unless you take some drastic approximations.
I suggest... either you find an animation of it online (shouldn't be hard). Or you learn to code and find a numerical solution.

 

[foxjwill]

err... I know how to code, but I can never seem to get my programs to work right. I know java, but I'm not sure if that's the best language to use for this. Any ideas?

 

[lzkelley]

I've used java and C++, and i find java to work well for programming simulations (at least for my purposes). The problem is going to be plotting in 3D. Java 2D works great, but i hear that 3D is pretty rough (though I've never tried it).

 

[foxjwill]

Ok, then, I'll look into java 3d. But what method(s) should I use for approximation?

 

[lzkelley]

Well, make the loops perfectly conducting, with a fixed constant current in each (should be going in the same direction).
From that you can use the Biot-Savart law to find the magnetic field everywhere--> you'll need to set up the B = integral_____... then use some method of numerical integration. the fourth order runga-kutta is the standard method for numerical integration, but i'd recommend a simple Euler's method (at least to start with). Once you have the magnetic fields everywhere, you can use the lorentz force equations to find the acceleration --> numerically integrate to find velocity --> and again to find positions as a function of time.
Does that make sense?
One simplification to start with, would be to only plot 2 of the 3 dimensions, it would surely give you something cool to look at!