Equilibrium: stable or unstable, that is the question...

A uniformly charged ring of radius $$R$$ with linear charge density $$\lambda$$ lies on the ground. Above it, along its axis, hovers a particle of mass $$m$$ and charge $$q$$. The particle is in equilibrium.

Describe the equilibrium of the particle:

(i) If the separation between the charged particle and the centre of the ring is less than $$\dfrac{R}{\sqrt{2}}$$

(ii) If the separation between the charged particle and the centre of the ring is greater than $$\dfrac{R}{\sqrt{2}}$$

Details & Assumptions

1. The ring retains its charge; it is not lost to the ground.
2. A uniform gravitational field $$\vec{g}$$ is acting downward.
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