One half of a charged thin ring of radius \(R\) carries a charge \(q_{1}\) uniformly distributed over it, and the other half of the ring carries a charge \(q_{2}\) uniformly distributed over it. For any position along the axis of symmetry of the ring, derive an expression for (a) the component of the electric field parallel to the axis and \((b)\) the component of the electric field perpendicular to the axis.