## deflection of plasma stream near magnetically-responsive surface

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

I'm trying to work out a theoretical problem, and I don't know how to approach it. Suppose I have a charged gas that is traveling near the surface of a magnetically-responsive solid.

I would expect the charged gas to be generating a magnetic field. I would also expect for the lines of force in the magnetic field to intersect with the solid at right angles, as in the diagram below.

Code:
Plasma stream is moving toward you.
The gas is positively-charged, so the magnetic field
will have CCW lines of force (right-hand rule).

----------
/   plasma   \
|    stream    |
----------------------------------
|  magnetically-responsive solid |
|                                |
----------------------------------
2. Relevant equations

?

3. The attempt at a solution

The question is: will the plasma stream be deflected in its movement toward the solid? In other words, will the stream tend to "hug" the surface? The hypothesis here is that the magnetic field generated by the plasma stream will exert force on magnetically-responsive particles in the solid. If those particles were free to move, they'd be accelerated around the plasma stream (or the plasma stream would be accelerated around them, depending on which was heavier). But the particles in the solid can't move, so they exert back-pressure on the magnetic field, which in turn alters the movement of the plasma. But in addition to this rotational acceleration, will the plasma experience a "drag" force as its magnetic field intersects with a stationary object? If so, then the plasma stream would be deflected toward the solid, and would tend to "hug" the surface of the solid as it traveled along it.

I'm just not sure how to approach calculating this force (if in fact it exists). Can somebody point me in the right direction?

-- Charles
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 Yeah, they would experience a force. If the charge on each particle of the gas is q, and it travels with a velocity v, then the force is $$F=q\vec{v}\times\vec{B}$$ which is the Lorentz force. Since youre assuming that B and V are perpendicular, F=qvB is the magnitude of force per particle and direction is given by Flemings left hand rule.

 Quote by chaoseverlasting Yeah, they would experience a force. If the charge on each particle of the gas is q, and it travels with a velocity v, then the force is $$F=q\vec{v}\times\vec{B}$$ which is the Lorentz force. Since youre assuming that B and V are perpendicular, F=qvB is the magnitude of force per particle and direction is given by Flemings left hand rule.
Thanks so much for responding!

I'm looking for a force beyond the Lorentz force. I think that in my thought experiments, I've come to the conclusion that it does not exist. Nevertheless, I have a phenomenon that I can't explain except with EM, and I'm just trying to figure out HOW it's EM. ;)

The idea was that a gas traveling near a solid would generate a Lorentz force that would act on the gas instead of the solid, because of the differences in mass, but ALSO, that there would be a drag force exerted on the gas (like surface friction, but for EM reasons). The moving particle will generate a magnetic field that will exert force on stationary particles in the solid, but because of the differences in speed, the influence of the magnetic field will accelerate the stationary particle and/or decelerate the moving one. Because this "drag force" would be only on one side of the gas, the result would be a deflection of the movement of the gas, toward the surface of the solid. Hence the gas would hug the surface as it moved along it.

But I think that this is just wrong. I got the idea from what were probably just sloppy descriptions of the behavior of Birkeland currents. The Lorentz force is sometimes represented as a spiral instead of a circle. But the Lorentz force is perpendicular, and there is no longitudinal component to it. Anyway... ;)

After penning my poorly-founded question, I got another idea. A charged gas traveling near a solid will generate a magnetic field, whose lines of force will intersect with the solid at right angles. In this situation, the magnetic pinch effect will do two things: it will consolidate the gas itself, but it will also bind the gas to the surface of the solid. Shortening of the lines of magnetic force will pull the gas toward the solid. So I'm going to play around with this idea for a while.

Does this make any sense?

Thanks so much for your time!