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Integrating over a cross product?

  1. Nov 2, 2015 #1
    Lets look at the force on a wire segment in a uniform magnetic field

    F = I∫(dl×B)

    I am curious if, from this, we can say:

    F = I [ (∫dl) × B] since B is constant in magnitude and direction
     
  2. jcsd
  3. Nov 2, 2015 #2

    blue_leaf77

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    Yes, we can.
     
  4. Nov 2, 2015 #3
    can you offer a proof?
     
  5. Nov 2, 2015 #4

    blue_leaf77

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    As you said, if you suppose ##\mathbf{B}## to be constant in direction and uniform, then it can be taken outside the integral.
     
  6. Nov 2, 2015 #5

    Nathanael

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    In essence, it is the same as doing this:
    L1×B + L2×B + ... = (L1 + L2 + ... )×B
    Which is the distrubative property of cross product.
    (That's not a proof of course; I just want to make sure the idea is clear.)
     
  7. Nov 2, 2015 #6
    This is how I arrived at my original idea, just wasn't sure if was applicable to integration.
     
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