3-dimensional charge density for a finite thin wire

[mjordan2nd]

Homework Statement

Express the 3D charge density $$\rho$$ for a thin wire with length Z and uniform linear charge density $$\lambda$$ 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

$$Q=\int^{Z}_{0}\lambda dz$$

This integral just evaluates to $$\lambda Z$$.

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

Thanks.

 

[kuruman]

Do you know what a Dirac delta function is/does? You may wish to check

http://en.wikipedia.org/wiki/Dirac_delta_function