# Equations for Arc Plasma near Magnetic Fields

1. Feb 29, 2004

### Rose Tinted Glasses

Hi, I'm currently doing an research experiment into the behaviour of plasma around magnetic fields. I will be using an arc welding machine for the plasma and an electromagnet. (So I can adjust the field's intensity as an independant variable.) The arc should bend in the presence of a magnetic field, and the how much it bends is dependant on the strength of the field. What I need to do is to be able to calculate/predict how much the plasma will bend if I know;
*The momentum of the plasma,
*The magnitude of the magnetic field,
*The kinetic energy of the plasma,
*The heat energy caused when the plasma strikes a surface.

Firstly, is there any way I can calculate the momentum and the kinetic energy if I know the heat energy given off when the plasma strikes a surface? If not, is there any other way I could find the plasma's p and KE?

And, furthermore, (and more importantly,) is there any way, to calculate how much the arc bends once I know the momentum, kinetic energy and magnetic field magnitude? If not, what should I be measuring to calculate how much the arc bends?

I can deal with rather complex maths, but, as I'm only a highschool freshman and haven't learned too much calculus, the simpler the better.

Regards;
-Alice.

PS: Sorry if this doesn't make a lick of sense, I may have gotten a bit mixed-up somewhere along the line. I'm relatively new to physics, you see.

EDITED: To spare you all some tedious background info on yours truly.

Last edited: Feb 29, 2004
2. Mar 1, 2004

### Haelfix

Dear Alice, I assume this is for a science project or something.

While your idea is good, its going to be hellish to pull off experimentally.

First problem
1) You need a huge magnetic field to observe bending of a relatively midly charged plasma. I say midly charged, b/c it won't stay ionized very long in air.
2) The magnetic field needs to be nice and uniform, or else all hell breaks loose for predictivity. In other words, you need a big solenoid not found in your local Kmart!
3) The plasma itself is molecularly complicated in your example, it will also interact with air particles, since it doesn't live in a relative vacuum. Eg you really want to do this experiment with a very pure plasma of a simple particle species, in a vacuum =D
The problem is, getting a decent vacuum is not something you can find in your local Kmart either!
4) You also want a very controlled emission. Say a very nice and uniform jet of plasma, so that the mean velocity doesn't have error bars that are off the chart.

The point is, its too hard a project for a high school student. What you can do however, is to derive some theoretical predictions for various plasma jets. This is usually acceptable work for a science project, in which case everything can be treated ideally. Ask again for more details

3. Mar 1, 2004

### chroot

Staff Emeritus
The only equation you need is the Lorentz force law:

$$F = q(\vec E + \vec v \times \vec B)$$

When the electric field, $\vec E$ is zero, this reduces to simply:

$$F = q( \vec v \times \vec B)$$

- Warren