Spherical capacitor with charge Q?

[center o bass]

If you have a spherical capacitor consisting of a metal sphere at an inner radius and an outer metal shell at an outer radius.. then you apply a constant voltage over the two plates.

Why is it so that the two metal plates will have the same total charge? Is this by conservation of charge?

Im thinking that it might be because if +Q goes to one sphere and charge can not be created, so therefore -Q has to go to the other? Is this correct?

 

[center o bass]

I think I was a bit too fast posting this question :)
I figured it must be because the two conductors are connected such that a current of charge runs from the one to the others. Hence -Q goes to one leaving the other with +Q.