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Biot Savart Law with a surface current

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    There is a disc with radius R which has a uniformly-distributed total charge Q, rotating with a constant angular velocity w.

    (a) in a coordinate system arranged so that the disc lies in the xy plane with its center at the origin, and so that the angular momentum point in the positive z direction, the local current density can be written J(x,y,z) = K(x,y) d(z). determine the surface current K(x,y) in terms of Q, w, and R.

    (b) using the Biot Savart law, determine the magnetic field at point r=sk, k is the vector direction. find the same for r=-sk.


    2. Relevant equations
    Biot Savart Law


    3. The attempt at a solution

    I obtained K= Q(w X R) / pi*R squared for part A, but I'm not sure how that's supposed to fit into the Biot Savart Law.
     
  2. jcsd
  3. Dec 9, 2008 #2
    Note that the velocity of the current is not equal for charges at R/2 as it is for charges at R (the angular velocity is the same, but the radii are different). Try modeling the solution as a sum of current loops of width dr, with approximately equal radius (and thus velocity)

    This answer would then be the current, which can be modeled with the Biot-Savart law.

    ~Lyuokdea
     
  4. Dec 9, 2008 #3
    Ok, I've done this and after applying Biot Savart's Law, I get a zero magnetic field. This can't be right can it?
     
  5. Dec 9, 2008 #4
    that doesn't sound right....what did you get for J, and how did you include this into the biot savart law?

    ~Lyuokdea
     
  6. Dec 9, 2008 #5
    nevermind, i looked at it again and found my mistake. thanks!
     
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