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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