 371
 11
 Homework Statement

Two rings with radius r have charge Q and −Q uniformly
distributed around them. The rings are parallel and located a
distance h apart, as shown in Fig. 1.35. Let z be the vertical
coordinate, with z = 0 taken to be at the center of the lower
ring. As a function of z, what is the electric field at points on
the axis of the rings?
 Homework Equations
 Coulomb Law
Hi! I need help with this problem. I tried to solve it like this:
First I calculated the electric field of each ring:
Thus the electric field at a point that is at a distance z from the ring is ##E=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}##, Thuss for the upper ring, the electric field would be ##E_1=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}## and for the lower one, it would be ##E_2=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}##.
Then, I choose a random point between the both rings, at a z height, so ##E_1=\frac{Q(hz)}{4\pi\epsilon_0((hz)^2+r^2)^{3/2}}## and
##E_2=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}##, so the total electric field would be the sum of both, right? ##E_t=\frac{Q}{4\pi\epsilon_0}\left(\frac{z}{(z^2+r^2)^{3/2}}\frac{(hz)}{((hz)^2+r^2)^{3/2}}\right)##.
The problem is that my answer is wroing and I don't know why. Hope someone can help me.