Helmhoz coil - Define the magnetic field

I have to calculate the magnetic field at point x = R/2 (R is the separation between the two coils).

I see why, for one coil, we only take the component along x from the B field as the values along y "cancel" themselves.

But if we add another coil on the other side, the values along x should also cancel themselves (since they have the same intensity at x = R/2)!

I really don't get why it's not 0 at point x = R/2. Here's a scheme of my understanding (with in red the dB field from the other coil)

If something is unclear please let me know.

• What direction is the current flowing in the other coil? Hint: one direction makes a Helmholtz coil and the other makes something significantly less useful. – ARM Jan 19 '15 at 18:19

I believe that you are talking about two parallel circular coils separated a distance $R$ along the $x$ axis, right? If this is the case the field would cancel if the currents circulating the two coils had opposite directions, and that is because the lines of the magnetic field go in the same direction in both sides of a coil (for large $x$) as depicted in this image: