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iScience
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why was maxwell given the credit to gauss's integral (flux) equation?
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.iScience said:why was maxwell given the credit to gauss's integral (flux) equation?
WannabeNewton said: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.
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.vanhees71 said: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.
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.]iScience said: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
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:vanhees71 said:I think Maxwell's theory is the most important achievement of classical physics since Newton's Principia.
It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.
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.Jolb said:Even the equation you mentioned has physical content: remember that Gauss' law only applies for conservative fields.
Maxwell was given credit for Gauss's integral equation because he was the first to publish a complete and correct form of the equation in his paper "A Dynamical Theory of the Electromagnetic Field" in 1864. While Gauss had developed the equation earlier, it was not published until after Maxwell's work. Furthermore, Maxwell's work included additional insights and applications of the equation, solidifying his contribution and earning him the credit.
It is believed that Gauss was aware of the significance of his integral equation, as he discussed its applications in his unpublished notebooks. However, it was not until Maxwell's publication that the equation gained widespread recognition and understanding.
No, Maxwell did not discover the integral equation independently. He was well-versed in the works of other scientists, including Gauss, and was likely influenced by their ideas and theories. However, Maxwell's contribution in formulating the equation in a complete and correct form and applying it to his own theories earned him the credit.
While Maxwell is the most commonly credited scientist for the integral equation, there have been others who have made contributions to its development and understanding. This includes Gauss, as well as other scientists such as Ampere, Faraday, and Green.
The integral equation has had a significant impact on the field of electromagnetism, as it serves as a fundamental tool for understanding and solving problems related to electric and magnetic fields. It has been used in the development of various theories and laws, such as Maxwell's equations, and has played a crucial role in the advancement of technology, including the development of devices such as antennas and electric motors.