Question: A sphere of radius $a$ is made of a nonconducting material that has a uniform volume charge density $\rho$. A spherical cavity of radius $b$ is removed from sphere which is a distance $z$ from the center of the sphere. Assume that $a > z + b$. What is the electric field in the cavity?
I understand the solution but what puzzles me is that if i apply the Gauss theorem to the cavity the electric field must be 0? many thanks in advance