OPtimization

[mugzieee]

a circular ring of wire radius r lies in a plane perpendicular to the x-axis and is centered at the origin. The ring has a positive electric charge spread uniformly over it. The electric field in the x-direction, E, at the point x on the x-axis is given by E= kx/(x^2 + r^2)^(3/2) for k>0. At what point on the x-axis is the field greatest? Least?

After taking the first derivative i ended up with:
E' = k(-2x^2 + r^2 - 3xr)/(x^2 + r^2)^(5/2)
i know after the derivative im supposed to find the critical points then classify them and find the global min and global max, but for critical points i end up with only a zero, waht does it look like is wrong here?

[Naeem]

The Important thing to know is that , The charge on a conductor ( in this case the circular ring ) resides on its outer surface. Therefore, electric field E inside the ring is zero.

2nd, For a point on the charged spherical conductor or outside it, the charge may be assumed to be concentrated at its centre.

Based on this least E which is zero, inside the ring.

The greatest is outside, the ring.

I hope this helps.

I don't know if you really need to take the derivative in this question. This seems more like a conceptual problem.