Two identical thin ring, each of radius R meters, are coaxially placed a distance R metres apart. If `Q_1` coulomb, and `Q_2` coulomb, are repectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is

Explanation

`V_(A) = (1)/(4 pi in_(0)) [ (Q_(1))/(R ) + (Q_(2))/(sqrt(2) R)]`
`V_(B) = (1)/(4 pi in_(0)) [ (Q_(2))/(R ) + (Q_(1))/(sqrt(2) R)]`
`V_(B) - V_(A) = (1)/(4 pi in_(0)R) [Q_(1) ((1)/(sqrt(2)) - 1) + Q_(2) (1 - (1)/(sqrt(2)))]`
`= (1)/(4 pi in_(0)) ((Q_(2) - Q_(1)) (sqrt(2) - 1))/(sqrt(2) R)`
Work done in moving a charge `q` from `A` to `B`,
`W_(ArarrB) = q(V_(B) - V_(A)) = (1)/(4 pi in_(0)) .((sqrt(2) - 1)(Q_(2) - Q_(1) )q)/(sqrt(2) R)`