Where is the maximum electric field on the axis of a charged ring?

[leroyjenkens]

Homework Statement

Show that the maximum magnitude E_max of the electric field along the axis of a uniformly charged ring occurs at x=a/(sqrt2) and has the value Q/(6(sqrt3)πε₀a²)

Homework Equations

E=k_eΔq/r²

The Attempt at a Solution

I made the vertical components cancel along the axis from the top and bottom of the ring so that I just have the x-axis field, but I really don't know what else to do. I'm not even sure if that equation is the right one to use. This question seems to be made deliberately confusing.

 

[ehild]

Show your work in detail, please.

ehild