Two identical particles of mass m carry a charge `Q`, each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed v. The closest distance of approach be .

Explanation

At the distance of closed approach , both particles move with same velocity .
Momentum conservvation : `mv_(0) = mv + mv rArr v = v_(0)//2`
Energy conservation :
`(1)/(2) mv_(0)^(2) = (1)/(2) mv^(2) xx 2 + (1)/( 4pi in_(0)) .(q.q)/(r )`
`(mv_(0)^(2)) /(2) = (mv_(0)^(2))/(4) + (q^(2))/(4 pi in_(0) r )`
`(mv_(0)^(2))/(4) = (q^(2))/(4 pi in_(0) r) rArr r = (q^(2))/(pi in_(0) mv_(0)^(2))`