It is a well-known fact that Maxwell's Equations, along with Lorentz's Force Law, form a complete description of classical electromagnetism. But why is that? I mean, I can understand that Lorentz's Law is necessary for describing the interaction between matter and electromagnetic fields, and I also understand the meaning of the other four equations but could you please explain to me why it is that they say everything which needs to be said about electromagnetism? Is it because the four equations, using the concepts of divergence and curl, completely describe the spatial configurations of the electric and magnetic vector fields, and how they relate to charges and to each other? How do physicist know they're complete?