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 seperation r between them (treat as point charges and mass of `q_(2)` is m)

Explanation

When the seperation between the charges is r, the force between them is `F=(1)/(4pi in_(0)) (q_(1)q_(2))/( r^(2))`
Acceleration of `q_(2) = (F)/(m) = (q_(1)q_(2))/( 4 pi in_(0) mr^(2))`
`(dv)/(dt) = (dv)/(dt) ((dr)/(dt)) = (vdv)/(dr)`
`rArr ( vdv)/(dr) = (q_(1)q_(2))/( 4 pi in_(0)mr^(2))`
`int_(0)^(v) vdv=(q_(1)q_(2))/( 4pi in_(0) m) int_(r_(0)) ^( r) r^(-2) dr `
or `(v^(2))/(2) = (q_(1)q_(2))/( 4 pi in_(0) m ) |(-1)/(r ) |_(r_(0))^(r )`
`rArr v = sqrt((q_(1)q_(2))/( 2pi in_(0) m) {(1)/(r_(0)) - (1)/(r )})`