Field Motion

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 $b + c + d + e$

This is a part of my set Aniket's Electrostats Challenges