A small sphere of radius r₁ and charge q₁ is enclosed by a spherical shell of radius r₂ and charge q₂. Show that if q₁ 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 q₂ on the shell is.

According to Gauss’s law, the electric field between a sphere and a shell is determined by the charge q₁  on a small sphere. Hence, the potential difference, V, between the sphere and the shell is independent of charge q₂. For positive charge q1, potential difference V is always positive.