# Ring of Charge-how to maximize the Electric Field

1. Oct 1, 2009

### 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?

Last edited: Oct 1, 2009
2. Oct 2, 2009

### Redbelly98

Staff Emeritus
Re: Ring of Charge--how to maximize the Electric Field

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