Question

Bringing an external charge near a conducting sphere

Answer 1

If the sphere is initially uncharged, then the electric flux through its surface is zero, by Gauss' law. If we add just one point charge q′q′, then we will find a net flux through the surface, which is wrong. However, add a second charge q′′=−q′q″=−q′, then the net flux is given by the enclosed charge q′+q′′=0q′+q″=0, and all is well.