Two fixed, identical conducting plates \(α\) &\(β\) , each of surface area \(S\) are charged to \(–Q\) and \(q\), respectively, where \(Q > q > 0\). A third identical plate (\(γ\) ), free to move is located on the other side of the plate with charge \(q\) at a distance \(d\) . The third plate is released and collides with the plate \(β\) . Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst \(β\) & \(γ\) .

Find the velocity of the plate \(γ\) after the collision and at a distance \(d\) from the plate \(β\).

If \(v=(Q-\frac{q}{x})(\frac{d}{m \epsilon_0 S})^{\frac{y}{z}}\)

then, find \((x+y+z)\).

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