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## Homework Statement

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.

## Homework Equations

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

[tex]Q=\int^{Z}_{0}\lambda dz[/tex]

This integral just evaluates to [tex]\lambda Z[/tex].

I have no idea how to proceed. Any help would be appreciated.

Thanks.