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Charge density for a disk moving at constant velocity

  1. Apr 12, 2012 #1
    Problem Statement: I'm having some trouble understanding how to write charge densities using delta functions, particularly when they involve geometries other than Cartesian. So I have a disk moving with velocity v (along the z-axis) that has total charge Q, and I'm trying to write ρ(x,t) so that I can calculate the electric field (and eventually the Cherenkov radiation emitted by the disk).

    Attempt at a Solution So I think I'd write something like this: ρ(x,t)=Q/(pi*R^2)delta(z-vt). So I've got a uniform charge density over the disk, and it's zero except at the z-coordinate of the disk. But I don't know if I'm missing some factors out front, since I'm in cylindrical coordinates.

    If I'm not going about this the right way at all please enlighten me.
     
  2. jcsd
  3. Apr 13, 2012 #2
    You did it right, the metric of the z coordinate in cylindrical system is 1.
     
    Last edited: Apr 13, 2012
  4. Apr 13, 2012 #3
    Oh! I get it now. Thanks a bunch, you've cleared up all my confusion with when factors are needed.
     
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