# 3-dimensional charge density for a finite thin wire

1. Sep 23, 2009

### mjordan2nd

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

The three dimensional charge density is the total charge over a volume.

3. 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.

2. Sep 23, 2009