Dirac Delta function and charge density.

[calcisforlovers]

I have a line charge of length L and charge density /lambda on the Z-axis. I need to express the charge density in terms of the Dirac Delta function of theta and phi. How would I go about doing this?

 

[pam]

$$\rho=\lambda\delta(1-\cos\theta)U(L-r))/(2\pi r^2)$$,
where U is the unit step function, should be the charge density in spherical coordinates.