Electric field due to a distributed charge over a ring

[henry3369]

Homework Statement

.A ring-shaped conductor with radius a = 0.025 m has a total positive charge Q = 0.125 x 10^-9C uniformly distributed around it. The center of the ring is at the origin of coordinates O.

What is the electric field (magnitude and direction) at point , which is on the x-axis at x = 0.4m.

Homework Equations

dq = λ(ds)
Q = λ(2πr)
dE = ((k)(dq)/r²) * (r^)

The Attempt at a Solution

So I figured out how to solve the electric field using the equations above, but for some reason I am not getting 0 for the electric field in the y-direction. I know that it has to be zero because all the electric fields cancel out in the vertical direction so I'm assuming my value for r^ is incorrect. Is it supposed to be (0.4i^ + 0.025j^)/(r)? It seems like it should be ((0.4i^ + 0j^)/(r) in order to get 0 for the vertical direction. After solving I end up with E = (6.98i^ + 0.4364j^) and the electric field in the x-direction is correct, but I don't think there is supposed to be a field in the y-direction. So, can someone tell me if my value for r^ is correct?

 

[TSny]

... so I'm assuming my value for r^ is incorrect. Is it supposed to be (0.4i^ + 0.025j^)/(r)?

By drawing a figure you should see that $\hat{r}$ will have y and z components that vary as you integrate over the ring.