I little bit confused while I'm trying to convert a cylindrical charge distribution to spherical. The question is:
A uniformly charged thin disk of radius $a$ and surface charge density $\sigma$ placed at the $xy$-plane with its center at the origin. The disk is enclosed in a grounded conducting sphere of radius $b (b>a)$. Using the appropriate Green’s function, find the potential for all points inside the sphere.
First I need to convert that cylindrical distribution to spherical
$f(r)$ for r dependence and $\Theta$ is heavyside func. I'll integrate it over volume in spherical coordinates and equalize to $\sigma$$\pi$$a^2$ to decide $\rho(x).$
Now, am I have to add $1/r$ because of the metric from the beginning? And then that question came to my mind, what if I put a sphere with radius $a$ with $\rho $ inside a cylinder wiyh radius $b$, how can I convert this?