Confusion: Van de Graaff generator

[conquerer7]

My physics book explains a van de Graaff in this way:

A small conducting sphere of radius a and carrying charge q is located inside a larger shell of radius b that carries charge Q. A conducting path is momentarily established between the two conductors, and the charge q then moves entirely to the outer conductor, because the charge on a conductor always moves to its outer surface.

But in any actual machine, you'd have to punch a hole in the outer sphere to bring the charge inside; wouldn't that merge the inner and outer surfaces? You can't even apply Gauss' Law like usual because the Gaussian surface would have to pass through the hole, and there'd be a nonzero field there.

Am I just completely misunderstanding it?

Edit: In addition, since the potential of the outer shell is so big (and should be uniform throughout), why doesn't charge flow off it onto the belt?

 

[Meir Achuz]

The hole is small enough that its influence is negligible.