A particle of charge q is released from rest at a distance to on the axis of a uniformly charged ring having a
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Sine component of the force cancels out in pairs due to opposite particles in the ring.
So, cosine component of force dominates and the net force is in −x direction when −q charged particle is +x direction and vice versa.
And there is symmetry in the electric force on the charge particle placed on the axis of ring due to charged ring. So charge particle will oscillate between +2R and −2R about the centre of the ring
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