With Gauss's Law, if we take a uniformly charged hollow sphere for instance, the electric field inside the hollow sphere is 0 because there is no charge inside. However, what if this sphere is not uniform?
I got confused because I heard this from a physics professor that said that if the charges around the sphere were not uniformly distributed, then the electric field inside would not be zero. Why is that?
Just to add, obviously every conductor would distribute its charge in a uniform way, so this question would not be relevant because it would not be something seen in nature. However, suppose that it was possible to have it non-uniformly distributed, or that it is an insulator for instance. In my opinion, the electric field inside should still be 0 because if not, Gauss's Law would break! There is still no charge inside, so the electric field should be 0, is that correct? Maybe I am not taking in consideration something and I am wrong, but I would appreciate if someone can clear my confusion, thanks in advance.
Edit: I will elaborate a bit more in my question.
I can think of why the electric field inside could be non-zero, just that I don't understand why Gauss's Law says that the electric flux is still 0.
Suppose that you have an electric dipole (just two opposite charges in space, each equal in magnitude) separated by a distance 'd'. Then, it is obvious that in between these two charges there must be an electric field, flowing out of the positive charge onto the negative charge. However, if we make a Gaussian spherical surface in between the charges, with a radius 'r' smaller than 'd' (r < d, so that the imaginary sphere does not enclose any charge). Then, Gauss's Law says that if the charge inside is 0 then the electric flux is 0, but we know that there is an electric field in between these two charges! Maybe I have a misconception of Gauss's Law, and it would be great if someone could explain to me what is my mistake (because I know that I am wrong). Certainly the electric field in (E)(dA)cosx is not 0, and the area is neither 0 obviously, and 'x' is not 90º. The only explanation that I can think of is if the integral of that basically sums quantities and subtracts other quantities...