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Thread: Opposing magnetic fields.

  1. #1 Opposing magnetic fields. 
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    If I opposed similar poles of two magnets and introduced a diffuse cloud of ionized atoms into this space, would the ions tend to splay out in a planer arrangement?
    How flat would the horizon of opposing magnetic fields be? Or would this horizon be really lumpy, perhaps dynamic and not static? Even with permanent magnets?


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    Quote Originally Posted by GiantEvil View Post
    If I opposed similar poles of two magnets and introduced a diffuse cloud of ionized atoms into this space, would the ions tend to splay out in a planer arrangement?
    How flat would the horizon of opposing magnetic fields be? Or would this horizon be really lumpy, perhaps dynamic and not static? Even with permanent magnets?
    Gosh, it's been a long time, but I think the ions would experience a force according to the rate at which their trajectory cuts the lines of magnetic flux, which would be oriented at right angles to both the component of motion cutting the field lines and to the field lines themselves. The shape of the field lines in this case would splay out out in all directions from the areas between the poles and then would start to curve back towards the opposite pole of each magnet. So it seems to me what would happen would depend on the angle and point of entry of the ion cloud, and the kinetic energy distribution within it. It doesn't feel to me as if the result would be particularly elegant and simple, but I could be wrong.


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    Quote Originally Posted by GiantEvil View Post
    If I opposed similar poles of two magnets and introduced a diffuse cloud of ionized atoms into this space, would the ions tend to splay out in a planer arrangement?
    How flat would the horizon of opposing magnetic fields be? Or would this horizon be really lumpy, perhaps dynamic and not static? Even with permanent magnets?
    If you inject the ions of mass ]tex]m[/tex] and charge with velocity into the resulting magnetic field of induction they (the ions) will follow a trajectory that is found by solving the equation of motion:



    where is the position vector such that and is a function of time with the boundary condition .

    The above becomes a second degree differential equation. It can be solved for very restrictive conditions (static , uniform magnetic field) producing the equation of the trajectory:




    The problem arises commonly in particle accelerators.
    Last edited by Howard Roark; December 19th, 2013 at 12:13 PM.
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by GiantEvil View Post
    If I opposed similar poles of two magnets and introduced a diffuse cloud of ionized atoms into this space, would the ions tend to splay out in a planer arrangement?
    How flat would the horizon of opposing magnetic fields be? Or would this horizon be really lumpy, perhaps dynamic and not static? Even with permanent magnets?
    If you inject the ions of mass ]tex]m[/tex] and charge with velocity into the resulting magnetic field of induction they (the ions) will follow a trajectory that is found by solving the equation of motion:



    where is the position vector such that and is a function of time with the boundary condition .

    The above becomes a second degree differential equation. It can be solved for very restrictive conditions (static , uniform magnetic field). The problem arises commonly in particle accelerators.
    I think he or she is asking what this would look like for the scenarios in question, not for the maths. By the way, isn't the left hand side simply the force on the ion?

    My guess is the ions will either spiral rather untidily along the lines of flux emanating from the area between the poles, or be flung away from them, but I may be wrong about this. What do you think?
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    Quote Originally Posted by exchemist View Post
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by GiantEvil View Post
    If I opposed similar poles of two magnets and introduced a diffuse cloud of ionized atoms into this space, would the ions tend to splay out in a planer arrangement?
    How flat would the horizon of opposing magnetic fields be? Or would this horizon be really lumpy, perhaps dynamic and not static? Even with permanent magnets?
    If you inject the ions of mass ]tex]m[/tex] and charge with velocity into the resulting magnetic field of induction they (the ions) will follow a trajectory that is found by solving the equation of motion:



    where is the position vector such that and is a function of time with the boundary condition .

    The above becomes a second degree differential equation. It can be solved for very restrictive conditions (static , uniform magnetic field). The problem arises commonly in particle accelerators.
    I think he or she is asking what this would look like for the scenarios in question, not for the maths.
    The "maths" describe what happens to the ions.


    By the way, isn't the left hand side simply the force on the ion?
    No, the right hand side is the force. The Lorentz force. The LHS is the standard format of the LHS of the equation of motion.

    My guess is the ions will either spiral rather untidily along the lines of flux emanating from the area between the poles, or be flung away from them, but I may be wrong about this. What do you think?
    I do not guess, the correct term is "chaotic motion".
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    Quote Originally Posted by xyzt
    I do not guess, the correct term is "chaotic motion".
    So, I take it that a cloud of say, +ions, would not form a planer arrangement in a region of opposed similar magnetic fields?
    [- mag 1 +] (+ions) [+ mag 2 -]
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    Quote Originally Posted by GiantEvil View Post
    Quote Originally Posted by xyzt
    I do not guess, the correct term is "chaotic motion".
    So, I take it that a cloud of say, +ions, would not form a planer arrangement in a region of opposed similar magnetic fields?
    [- mag 1 +] (+ions) [+ mag 2 -]
    You must shoot them perfectly perpendicular to the two magnets, the smallest angle and they go chaotic. Even if you manage to shoot them perfectly, it is an unstable equilibrium, the smallest perturbation and they go chaotic. You have a much better chance with two infinite, perfectly planar, parallel magnetic plates.
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    Quote Originally Posted by xyzt
    You have a much better chance with two infinite, perfectly planar, parallel magnetic plates.
    Do you know where I could buy some of these?
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