Charge density for a disk moving at constant velocity

In summary, the conversation involved discussing how to write charge densities using delta functions in non-Cartesian geometries. The problem statement was about finding a way to calculate the electric field and Cherenkov radiation emitted by a disk moving with velocity v along the z-axis and having total charge Q. The solution involved writing the charge density as ρ(x,t)=Q/(pi*R^2)delta(z-vt) to represent a uniform charge density over the disk with a non-zero value only at the z-coordinate of the disk. The conversation also clarified that the metric of the z coordinate in cylindrical system is 1 and no additional factors were needed in the solution.
  • #1
Albereo
16
0
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.
 
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  • #2
You did it right, the metric of the z coordinate in cylindrical system is 1.
 
Last edited:
  • #3
Oh! I get it now. Thanks a bunch, you've cleared up all my confusion with when factors are needed.
 

Related to Charge density for a disk moving at constant velocity

1. What is charge density?

Charge density refers to the amount of charge per unit volume in a given area or space. It is typically measured in coulombs per cubic meter.

2. How is charge density calculated?

Charge density can be calculated by dividing the total charge by the volume it occupies. For a disk moving at constant velocity, the formula would be charge density = charge / (π * radius^2 * height).

3. Does the charge density change as the disk moves at constant velocity?

No, the charge density remains constant as long as the charge and dimensions of the disk do not change.

4. How does the charge density affect the electric field around the disk?

The charge density is directly related to the electric field strength around the disk. As the charge density increases, the electric field strength also increases.

5. Can charge density be negative?

Yes, charge density can be negative if the net charge on the disk is negative. However, in most cases, charge density is positive as objects tend to have more positive charges than negative charges.

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