Why there is no electric field outside of the sphere

[brad sue]

Hi, I need to understand something:

A point charge -q is fixed at the center of a hollw spherical conductor of charge +q. Draw the electric field lines both inside and outside.

Please can you explain me why there is no electric field outside the sphere?
thank you

 

[jamesrc]

If you're using Gauss' law to find the electric field, then the total electric flux out of your gaussian surface is proportional to the enclosed charge. If you add up the charge inside your gaussian surface (say, a sphere with a radius bigger than the spherical conductor), what is it? (what is -q + +q?)