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Charge `q_(1)` is fixed and another point charge `q_(2)` is placed at a distance `r_(0)` from `q_(1)` on a frictionless horizontal surface.Find the velocity of `q_(2)` as a function of separation `r` between them (treat the changes as point charges and mass of `q_(2)` is m)

Text Solution

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According law of conservation of energy
`U_(1) + K_(1) = U_(2) + K_(2)`
`(1)/(4pi in_(0)) (q_(1)q_(2))/(r_(0)) + 0 = (1)/(4pi in_(0)) (q_(1) q_(2))/(r ) + (1)/(2) mv^(2)`
`(1)/(2) mv^(2) = (q_(1) q_(2))/(4pi in_(0)) [(1)/(r_(0)) - (1)/(r )]`
`v = sqrt((q_(1)q_(2))/(4pi in_(0)m) [(1)/(r_(0)) - (1)/(r )])`
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