The integral form of gauss's law is used to determine the electric field of charge distributions which possess a certain amount of symmetry. Now imagine using it in situations where the gaussian surface includes equal amounts of positive and negative charge. For example,imagine a point positive charge surrounded with an spherical shell of negative charge of equal magnitude to the positive charge. Gauss's law predicts a zero field for outside of the volume of this configuration but I calculated it directly and saw that it has a non-zero field although it is weak and dies off so fast. This example leads me to think that gauss's law gives an approximation to the field in such situations and this makes me doubt about the nature of gauss's law. Any ideas?