A system consists of two concentric spheres, with the inside sphere of radius a carrying a positive charge `q_(1)`. What charge `q_(2)` has to be diposited on the outsie sphere of radius `b` to reduce the potentail `varphi` depend in this case on a distance `r` from the centre of the system ? Draw teh appoximate plot of this dependence.

Explanation

Potentail at the inside sphere,
`varphi_(a) = (q_(1))/(4pi epsilon_(0) a) + (q_(2))/(4pi epsilon_(0) b)`
Obviously `varphi_(a) = 0` for `q_(2) = - (b)/(a) q_(1)` ...(1)
When `r ge b`,
`varphi = (q_(1))/(4pi epsilon_(0) r) + (q_(2))/(4pi epsilon_(0) r) = (q_(1))/(4pi epsilon_(0)) (1 - (b)/(a))//r`, using Eq. (1).
And when `r le b`
`varphi_(r) = (q_(1))/(4pi epsilon_(0) r) + (q_(2))/(4pi epsilon_(0) b) = (q_(1))/(4pi epsilon_(0)) ((1)/(r ) - (1)/(a))`