A small sphere of radius `r_(1)` and charge `q_(1)` is enclosed by a spherical shell of radius `r_(2)` and charge `q_(2)`. Show that if `q_(1)` is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge `q_(2)` on the shell is [Fig]

Explanation

Electric potential inside the spherical shell is same as that on its surface. When the sphere is kept inside the shell then its potential becomes equal to the potential of the spherical shell. When additional positive charge is given to sphere then its potential increases due to its own charge and hence, it attains potential greater than that of the shell. Thus, when both of them are connected by a metallic wire then all charge of the inner sphere is trasferred to the shell so that both may attain the same potential. The same concept is used in designing a Van de Graaff generator. Charge of the spherical shell of the generator is transferred to it from inside. It is important to note that the pootential of interior conductor will be equl to that of the exterior shell only if charge on the inner sphere is zero.