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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