Difficult# Electric Field Above a Symmetric Arc of Charge

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Figure 1 depicts a symmetric arc of charge which lies in the $x$-$z$ plane.

All charges are at a distance $\rho = 4.20 \text{ cm}$ from the origin of coordinates, as you can see from Figure 2, which shows the $x$-$z$ plane in projection.

The line of charge has a linear charge density of $\lambda = 0.550 \; \mu \rm{\frac{C}{m}}$, extending from an angle $\theta_0 = +55.0^\circ$ with respect to the negative $z$-axis to an angle $\theta_f = +125^\circ$ with respect to the negative $z$-axis.

What is the magnitude of the electric field at a height of $h = 6.60$ cm above the origin of coordinates along the positive $y$-axis?