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The x-axis is the symmetry axis of a uniformly charged ring of radius R and charge Q. A point charge Q of mass M is located at the center of the ring. Show that the ultimate speed of the point charge is u = ((2kQ^2)/MR)^1/2
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When it is displaced slightly, the point charge accelerates along the x axis to infinity

Conserving energy, the inital energy is entirely electric,

initial energy = P E = kQ^2/R

because all the ring charge is a distance $R$ from the particle.

The final energy is entirely kinetic

Energy final = K E = 0.5 M v^2

initial energy = final energy

so
KQ^2/R = 0.5 M V^2

there fore

V =  ((2kQ^2)/MR)^1/2
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