Sample problem: Integrating effects of a continuous source

Consider a uniform ring of charge of radius r=1cm. Assume that the charge density is $1\mu C/cm$ and that the ring is a perfect circle, very thin, that it lies in the xy plane and is centered at the origin.

1.

Find and plot the electric potential energy on a test charge of size $q=-0.01\mu C$ as a function of distance on the z-axis.

2.

Find and plot (as a vector) the force on this same particle. Why is z=0 special?