Charge density for a disk moving at constant velocity

[Albereo]

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.

 

[sunjin09]

You did it right, the metric of the z coordinate in cylindrical system is 1.

 

[Albereo]

Oh! I get it now. Thanks a bunch, you've cleared up all my confusion with when factors are needed.