He wasn't. Where did you read that? He was given credit for other things, especially for his substantial contribution to the forging of a coherent framework of a theory of the classical electromagnetic field.
Well, it was Maxwell who 'united' Gauss' law with the other laws of electromagnetism, so the 4 laws are together known as Maxwell's laws. He wasn't really given credit for it, but I guess his name is mentioned a lot.
Actually Faraday's law is included in Maxwell's equations, too, but each man has his own credit. Usually science is fair.
i was referring to "maxwell's equations". the integral form of E-field divergence. i thought because it was part of maxwell's equations that he was given credit for it instead of gauss
Ah ok. As others said above, he was given credit for combining electricity and magnetism into a unified theory of the classical electromagnetic field, and this involved bringing together Gauss's law, Faraday's law etc. but the individuals still get credit for their laws.
I think Maxwell's most important contribution to E&M is twofold: First of all he mathematized Faraday's intuitive field picture and second he added the displacement current to Ampere's Law, leading to the prediction of electromagnetic waves and unifying electromagnetism with optics. I think Maxwell's theory is the most important achievement of classical physics since Newton's Principia. At the same time it was a paradigm shift from the idea of action at a distance to local field theories. Classical physics was completed with the advent of the theory of relativity. The special theory immediately emerged from the analysis of Maxwell's equations by Heaviside, Lodge, FitzGerald, Voigt, H. Hertz, Poincare, Lorentz, and finally Einstein. After this complete understanding of classical electrodynamics and "electron theory", the trouble with the atomistic structure of matter could be attacked on a solid basis of classical physics. I finally lead to the development of quantum theory and after all the Standard Model particle physics. This is also a direct generalization of (quantum) electrodynamics and thus can be traced directly back to Maxwell's and the "Maxwellian's" work on classical electromagnetism. I think I don't need to emphasize the more practical aspects of Maxwell's work :-).
I wouldn't say that QED gives a direct route to the rest of the 'standard model'. But I do agree it is the 'textbook' case, which happens to work very nicely. What I really like about Maxwell's work is that it brought so many seemingly different concepts together. Both simplifying and generalising.
Well there are four Maxwell's equations and you're just talking about one of them. The reason the equations are named after Maxwell rather than Gauss is because Maxwell's equations have a physical content that goes beyond the mathematics Gauss established. For example, there is absolutely no mathematical reason for another one of Maxwell's equations, [itex]\nabla\cdot\vec{B}=0[/itex], it is just an experimental fact. Even the equation you mentioned has physical content: remember that Gauss' law only applies for conservative fields. There is no mathematical reason that we observe the E field to be conservative; it is just another experimental fact. [Edit: there is an error in this last sentence. See below.] Well the development of statistical mechanics, particularly the concept of Entropy and the Boltzmann distribution, is an extremely important achievement of classical physics, primarily because of how fundamental those concepts are. It didn't need any corrections when people discovered QM, but EM did need to get its QED treatment. Even Einstein said of thermodynamics:
I would say much of the "bringing together seemingly different concepts" was done by Faraday. Maxwell made it mathematical but the famous experiments intimately linking magnetism to electricity were done by Faraday. Faraday was a god amongst physicists. Faraday.
A vector field need not be conservative in order for the divergence theorem to apply. ##\int (\nabla\cdot E) dV = \int E\cdot dA ## doesn't appeal to the fact that ##\nabla\times E = 0## for electrostatic configurations.
Yes, Wannabe, you are right, I misspoke. I should have said that the divergence theorem requires that the field have a continuous first derivative--there is no mathematical reason a priori why we don't observe the EM field with a discontinuous first derivative. It is an experimental fact.