Line of charge as a volume charge dist. (w/ Dirac delta fcn.)

[AxiomOfChoice]

How would you write an infinite line charge with constant charge per unit length $\lambda$ as a volume charge density using Dirac delta functions? Perhaps in cylindrical coordinates?

I'm confused because if you integrate this charge distribution over all space, you should get an infinite amount of charge...right?

And is there an easy way to do the same thing for a line of charge of length $L$ and $\lambda = Q/L$?

 

[Born2bwire]

You could define it as a piecewise function that uses Dirac deltas. You could define it as the superposition of two appropriate step functions that scale a Dirac delta.

*shrug*