Figure 1 depicts a symmetric circle of charge. The charges lie on a circle of radius $\rho = 5.40 \text{ cm}$ in the $x$-$z$ plane. The line of charge contains a total charge $q = 0.420 \; \mu\rm{C}$.

What is the magnitude of the electric field at a height of $y = h = 7.66$ cm above the origin of coordinates?