A thin, semi-circular nonconducting rod located in the upper half of the \(xy\)-plane (\(y > 0\)) is centered at the origin \(O\) and carries a uniform positive charge \(+Q\). At the origin, the electric field produced by this rod has magnitude \(E_0\) and points in the \(-y\)-direction. A second identical semi-circular rod carrying a uniform negative charge \(-Q\) is placed in the lower half of the \(xy\)-plane (\(y < 0\)) to complete a full circular ring. What are the magnitude and direction of the net electric field at the origin \(O\) due to both charged rods?