A thin insulating ring of radius a lies flat in the xy$-$plane with its center at the origin of the coordinate system. The right half of the ring carries a positive charge $\backslash (+2$ Q $\backslash )$ uniformly distributed over its length while the left half carries a negative charge $-$Q uniformly distributed over its length.

Derive the magnitude and direction of the electric field at the origin of the coordinate system $($use symmetry arguments when appropriate$).$ Show the steps of your derivation in detail so that you can earn points for the process as well as for the final result.