A thin nonconducting rod with a uniform distribution of positive charge $q$ is bent into a circle of radius $R,$ as shown in Fig. $2.$ The central perpendicular axis through the ring is a $z$ axis, with the origin at the center of the ring.

$($a$)$ What is the magnitude of the electric field due to the rod at $z=0?$ Explain.

$($b$)$ What is the magnitude of the electric field due to the rod at $z=?$ Explain.

$($c$)$ In terms of $R,$ at what positive value of $z$ is that magnitude maximum?

$($d$)$ If $R=8cm$ and $q=15C,$ what is the maximum magnitude?