Not Just Simple SHM

In the absence of a gravitational field and an external electric field, a thin rod carrying uniform charge \(-q\) is placed symmetrically along the axis of a thin fixed ring of radius \(R\). The ring carries a uniformly distributed charge \(Q\). The mass of the rod is \(M\) and its length is \(2R\). The rod is displaced slightly along the axis of the ring and then released. If the time period \(T\) of small amplitude oscillation is \(4\pi R\sqrt{\frac{(b\sqrt{a}\pi\epsilon MR}{Qq}}\), \(b\) and \(a\) being natural numbers, find \(b+a\).

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