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Magnetic bottle

  1. Apr 29, 2008 #1
    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

    [tex]d\textbf{B} = \frac{\mu_0}{4\pi} \frac{Id\textbf{l} \times \textbf{\hat{r}}}{r^2}[/tex]


    [tex]d\textbf{F} = q\textbf{v} \times d\textbf{B}[/tex]

    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.
  2. jcsd
  3. Apr 29, 2008 #2
    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.
  4. Apr 29, 2008 #3
    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?
  5. Apr 30, 2008 #4
    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).
  6. Apr 30, 2008 #5
    Ok, then, I'll look into java 3d. But what method(s) should I use for approximation?
  7. Apr 30, 2008 #6
    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!
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