Calculating Q such that E(0,0,0)=0

[falyusuf]

Homework Statement

Attached below.

Relevant Equations

Attached below.

Question

Relevant equation;

My attempt:

Could someone please confirm my answer?

 

[anuttarasammyak]

Electric field at the Origin contributed from half ring is of direction - y and its magnitude is expressed by integral
$$\frac{1}{4 \pi \epsilon_0} \int_0^\pi \frac{\rho r \sin\theta d\theta }{r^2}$$
where r is radius of half ring, $\rho$ is line density of its charge.

 

[Babadag]

The component radial is cancel out, because of all direction of component radial around circle center