Net charge of a spherical capacitor

[ksoileau]

Suppose we have a hollow spherical shell made of a conducting metal, inside a slightly larger hollow spherical shell made of the same conducting metal. The shells are separated by a layer of insulation, so that the assembly is basically a spherical, hollow capacitor. If I cause the inner shell to have a negative charge of, say, 1 Coulomb, and the outer shell to have a positive charge of 1 Coulomb, what is the net charge on the assembly? Is it zero or is it equal to the charge on the outer shell?

 

[mfb]

The net charge is the sum of all charges of the setup.