# Magnetic bottle application

• foxjwill
In summary, Biot-Savart law can be used to find the magnetic field in a region between two coaxial circular loops of wire. However, this method is not accurate and might require approximations.

#### 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.

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.

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?

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).

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

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!

## 1. What is a magnetic bottle and how does it work?

A magnetic bottle is a device that uses magnetic fields to confine charged particles, such as plasma, in a specific area. It works by creating a region of high magnetic field strength, known as the "bottle," which traps the particles inside. This is achieved by using magnetic coils or permanent magnets arranged in a specific configuration.

## 2. What are the applications of a magnetic bottle?

Magnetic bottles have a wide range of applications in various fields such as fusion research, particle accelerators, and plasma physics. They are also used in industrial applications, such as in the production of semiconductor chips and in the purification of metals.

## 3. What are the advantages of using a magnetic bottle?

One of the main advantages of using a magnetic bottle is that it can confine particles without any physical contact, which eliminates the risk of contamination. Additionally, magnetic bottles can create high-density plasmas and can be easily manipulated and controlled, making them useful for various experiments and applications.

## 4. Are there any limitations to using a magnetic bottle?

One limitation of a magnetic bottle is that it can only confine charged particles, which limits its applications to plasma or ionized gas. Additionally, the strength of the magnetic field required for containment can be energy-intensive and expensive to produce.

## 5. How is the strength of a magnetic bottle determined?

The strength of a magnetic bottle is determined by the strength and configuration of the magnetic field. The field strength is measured in units of Gauss or Tesla, and the shape and size of the bottle can also affect the strength of the confinement. Additionally, the properties of the particles being confined, such as their charge and mass, can also impact the strength of the magnetic bottle.