A thin fixed ring of radius \(a\) has a positive charge \(q\) uniformly distributed over it . A particle of mass \(m\), having a negative charge \(Q\) , is placed on the axis at a distance of \(x (x<<a) \)from the centre of the ring . Find the Time period of oscillations (SHM) if it is displaced a little.

Your answer can be represented as

\[\large {\left(\frac {e \pi^b {\epsilon}_{○} m a^c}{qQ}\right)^d}\]

Where b , c , e are positive integers and d is a positive rational number

Enter your answer as \( b + c + d + e\)

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