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Biot-Savart's law application

  1. Dec 11, 2016 #1
    1. The problem statement, all variables and given/known data
    There's a disc with a current density surface σ, with radius R and angular velocity ω szajxv.png
    Find the B

    2. Relevant equations
    α = vσ=ωrσ
    13ygdj5.png
    3. The attempt at a solution
    I'm having problems understanding why the cross product gives αr
    2ebwnqx.png
     
  2. jcsd
  3. Dec 11, 2016 #2

    Charles Link

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    Homework Helper

    ## \vec{u_r} ## is a unit vector. The cross product ## \vec{\alpha} \times \vec{u_r} ## is simply ## \alpha \hat{z} ##. Write out the expression for ## dS' ## in terms of ## dr ## and ## d \theta ## and I think you will see where the "r" in the numerator comes from. Also, express ## \alpha ## in terms of ## \sigma ## and ## r ## and ## \omega ## . (## \alpha ## is not a constant). ## \\ ## editing... Your diagram is hard to read, but I see the disc extends out to radius R. (I initially thought the disc goes from ## R_1 ## to ## R_2 ##.) ## \\ ## Once you get these steps in place, you can then evaluate the integrals.
     
    Last edited: Dec 11, 2016
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