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> I am trying to find the electric potential of a rod with the following charge density function:
> $$\rho (\vec r)=k\delta(x)\delta(y)\theta(a - |z|).$$
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From the way that the charge density function looks like, I can understand that the rod has no radius in the xy-plane and it stretches from -a to a in the z- axes.

I am trying to find the electric potential in cylindrical coordinates $\Phi(\rho , \phi,z)$ by using the known equation for it:

$$\Phi(\vec r)= \frac {1 \cdot k}{4 \pi \epsilon\_0} \cdot \int\_V \frac {\rho (\vec r)}{|\vec r - \vec r'|}$$.

But the problem I am facing is that I don't know how to manage the delta function in cylindrical coordinates.That's why I thought of trying to solve the equation in cartesian and then convert in cylindrical but that doesn't work either, or maybe it's to difficult for me. So I thought of doing it the way I said above, by using cylindrical coordinates, but I am unfamiliar with how delta works in this case because $\delta (x)$ in cylindrical becomes $\delta (\rho \cos \phi)$ and I don't know how the integration works in this case. Can anyone give me tips on how to proceed past this point ?