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Assume we have a rod of diameter $d$ and length $l$. It is filled with a mixture of water and, say, sodium chloride. Thus there are positively charged sodium ions and negatively charged chloride ions in the water.

Now, assume that the rod is rotated perpendicular to the ground. I should add that the rotation happens at the mid point, not at one of the ends. Earth's magnetic field $B$ thus asserts force to the moving particles according to $q (v \times B)$ (Lorentz force).

This means (I think) that the particles should start to move to the ends of the rod. If the rotation is in counterclockwise direction, the right hand rule states that positive particles should move to the right side and opposite for negative. (I think)

Question is, does this really happen or is the centrifugal force going to push the particles to the sides? If so, how strong magnetic field $B$ or the velocity $v$ should be in order for this to happen?

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Be careful that you will also have a driving force for flow. More info: en.wikipedia.org/wiki/Magnetohydrodynamics –  Bernhard Feb 24 '13 at 0:22
    
@Bernhard Ah, so when the solution itself moves, it induces a current in itself and thus affects itself in this way? –  Valtteri Feb 24 '13 at 0:34
    
Do you mean that the rod is spinning about its own axis (moment of inertia $I=m d^2/8$) or about the midpoint of it's length (with moment of inertia $I=m l^2/12$)? –  KDN Feb 24 '13 at 0:36
    
@KDN The axis of rotation is attached to the midpoint along the length of the rod. Thus $I = m l^2/12.$ –  Valtteri Feb 24 '13 at 0:40
    
Chat with me for a minute: chat.stackexchange.com/rooms/7649/mhd-spinning-rod –  KDN Feb 24 '13 at 0:52
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1 Answer

up vote 3 down vote accepted

The simple answer is that, if the rod is really full of an incompressible fluid, the centrifugal force will be balanced by a pressure gradient and will not, on its own, create a fluid flow. If the magnetic field is parallel to the axis of rotation, then it will tend to drive one charged species toward the ends of the rod, while the other charged species is driven toward the center of the rod (near the rotation axis). These accumulations will be opposed by the electric field that arises as the ion species segregate, which will limit how strong a concentration gradient may develop.

All of this is confounded by the fact that a rotating rigid vessel creates shear forces on the fluid contained within. The fluid viscosity, fluid temperature, the precise strength of the magnetic field and the rotation velocity, the ratio of $l$ to $d$, the ratio of the mean free path to the rod size... all of these variables become relevant to the magnetohydrodynamic model of the system you have described, and the result is very complex.

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