# Potential generated by an ionized plasma between two plates

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1. Dec 4, 2013

### MeMoses

1. The problem statement, all variables and given/known data

An ionized plasma flows with a velocity v in the z direction, though a rectangular pipe with x, y, z dimensions of w, h, l respectively. The walls at $x=\pm w/2$ are insulating while the walls at $y=\pm h/2$ are conducting. Lastly there is a magnetic field B in the x direction.

Find the potential between the conducting walls.

2. Relevant equations

Maxwell's equations

3. The attempt at a solution

I'm not used to problems with plasmas, but I take it the velocity somewhat similar to current here. I'm not sure what I need to find the potential though, perhaps the electric field between the plates, but then I'm not sure where to find that. I think my main problem is I'm just not sure where to start. Any help would be appreciated.

2. Dec 4, 2013

### voko

Plasma consists of charged particles. Consider one of them, with charge q. It is said to flow with velocity v in the z direction. That means the net force on the particle is zero. But there are a magnetic field and an electric field, both exerting forces on it.

3. Dec 4, 2013

### MeMoses

Yea that really simplifies things from how I was approaching it. So $F_{mag} = F_{electric}$
$$EQ=Q(v \times B)$$
$$E=-vB$$
so then
$$V = hBv$$

4. Dec 4, 2013

### voko

Not exactly. Rather, it is $F_e + F_m = 0$. So check the signs in what follows.