Express the 3D charge density [tex]\rho[/tex] for a thin wire with length Z and uniform linear charge density [tex]\lambda[/tex] along the z-axis in terms of a two-dimensional dirac-delta function.
The three dimensional charge density is the total charge over a volume.
The Attempt at a Solution
I am not sure how to proceed with this question. Last night I attempted to calculate the electric field components, which I believe I did correctly, but was heavy in the algebra. I had intended to use Gauss law to calculate the charge density from the Electric field, hoping that a delta function would pop out somewhere. I talked to my professor today and he told me I was using the wrong approach, and that the solution to this problem is much simpler. Unfortunately I'm not sure I entirely understand how to use the dirac-delta function, and I feel stuck. I'm not sure how to start this problem. All I know is that
This integral just evaluates to [tex]\lambda Z[/tex].
I have no idea how to proceed. Any help would be appreciated.