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.

Explanation

The potential of the outer spherical shell
`V_2={:("potential due to "),("its own charge " q_2):}+{:("potential due to"),("inner charge "q_1) :}`
The potential of the inner solid sphere is
`V_1={:("potential due to "),("its own charge " q_1):}+{:("potential due to"),("inner charge "q_2) :}`
`=1/(4pi epsi_0) (q_1/r_1 + q_2/r_2)`
`:. V_1 -V_2 = q_1/(4pi epsi_0)[1/r_1 - 1/r_2] = (q_1(r_2-r_2))/(4pi epsi_0 r_1r_2) = + ve`
As positive charge flows from higher potential to lower potential, hence charge will necessarily flow solid sphere to spherical shell, when the two are connected by a wire.