A positive charge Q is uniformly distributed along a circular ring of radius R. A small  test charge q is placed at the centre of the ring then

If q>0 and is displaced away from the centre in the plane of the ring, it will be  pushed back towards the centre

If q<0 and is displaced away from the centre in the plane of the ring, it will never  return to the centre and will continue moving till it hits the ring

If q<0, it will perform SHM for small displacement along the axis

q at the centre of the ring is in an unstable equilibrium within the plane of the  ring  for a>0