Gauss's Law in Physics

Coulomb's law tells you the field of a single charge, and adding up thousands of those contributions is possible but rarely pleasant. Gauss's law replaces the adding with a piece of geometry. Wrap any closed surface around a charge and the field lines poking out through it always carry the same total, no matter what shape you chose, because field lines can only begin and end on charge. That makes the law a shortcut for anything with enough symmetry, a sphere, a long cylinder or a broad sheet, and it gives the whole story of conductors in a couple of lines, which is why it also explains why the field inside a conductor is always nothing.