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Electromagnetism, calculation of B

  1. Jun 1, 2014 #1
    1. The problem statement, all variables and given/known data
    A very big iron plate with the thickness 2h have, far from the plates edges, had a hole with the radius a drilled through it. With respect to the holes axis of symmetry the plate has a magnetization

    [tex]\bar{M} = M_0 \frac{a}{s} \hat{s}[/tex]

    where s is the distance from the axis of symmetry.

    In the hole, centered around the axis there is a small circular conductor with the current I with radius b << a.

    Find the force on the conductor.


    3. The attempt at a solution

    I went ahead and found the bound charges which proved to be only on the top and bottom surfaces which proved to be

    [tex]\bar{K} = M_0 \frac{a}{s} -\hat{\phi}[/tex] for the upper surface and the same in the reversed direction for the lower.

    Now with simply the right hand rule I concluded that the only B which will give a net force is the one in the s direction (giving a force in the z direction). The force from phi disappears in the cross product of biot savart, the force from z disappears due to symmetry. Then using with the knowledge that the only force that matters is the z component of the force:

    [tex]\bar{F} = \Delta(\bar{m} \cdot \bar{B}) = \bar{m} \cdot \frac {d \bar{B}}{dz}\hat{z}[/tex]

    So I get that due to m being dotted with B only the z component survives of B, but I also concluded that the z component of B would not give a net force. Yet it ends up being the only one that gives a net force? There's something I'm misunderstanding 100% here.

    and seems my tophats aren't working, but they're the unit vectors
     

    Attached Files:

    • hole.png
      hole.png
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    • B.png
      B.png
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    Last edited: Jun 1, 2014
  2. jcsd
  3. Jun 1, 2014 #2
    For hats use \hat instead of \^.
     
    Last edited: Jun 1, 2014
  4. Jun 1, 2014 #3
    That worked, thanks.
     
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