Ring of Charge-how to maximize the Electric Field

[lu6cifer]

Ring of Charge--how to maximize the Electric Field

A thin nonconducting rod with a uniform distribution of positive charge Q is bent into a circle of radius R. The central perpendicular axis through the ring is a z-axis, with the origin at the center of the ring.


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




After going through the integration, the equation for a ring of charge is

k*(Qz / (z²+R²)^3/2))





Edit: So, with some help, I realized that to maximize the function, I'd have to differentiate...
But what am I differentiating with respect to? z? r? And I know k is a constant; are everything else non-constants?

 

[Redbelly98]

You're looking for the value of z which maximizes the function, while the size of and charge on the ring are constants.