# Maxwell equations [closed]

$$\oint B.dl = \mu_0\left(I+\epsilon_0\frac{\partial\Phi_E}{\partial t}\right)$$ Please explain the applications , and implications of the modified Ampere's circuital law with Maxwell's addition. Especially, significance of Maxwell's work

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## closed as too broad by jinawee, Nathaniel, Robin Ekman, John Rennie, JamalSJun 12 at 11:47

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'+1' to counter the silent downvotes. –  user31782 Jun 12 at 10:17
@user31782 "There will be fun, not humiliation. A community website free from some old cranky farts" LOL and go for it! Fantastic idea: I do think that the worth of spreading science to everybody, not just the initiated, can too often get lost. I'm 50 and hopefully, if I'm not too cranky, I might take a look sometime :) –  WetSavannaAnimal aka Rod Vance Jun 12 at 11:23
@WetSavannaAnimalakaRodVance There are different opinions on how this forum should respond to questions like this. Those who feel that it is inappropriate point to the mission of this group, where it says "We're a little bit different from other sites." There are plenty of forums where this question would not generate negative reactions, and be warmly welcomed. Here's one, here's another, here's a third. But opinions differ. –  garyp Jun 12 at 12:30

See my answer here: Maxwell's big contribution was the notion of displacement current, which then changed the equations of electromagnetism in a way that foretold electromagnetic radiation whereby the Cartesian components of the fields all fulfilled D'Alembert's Wave equation and moreover that the wavespeed $c$ would be $c = 1/\sqrt{\mu_0\,\epsilon_0}$. The latter's ($c$, that is) surprising nearness to the experimentally known value as found by the Fizeau experiment led Maxwell to assert that light is one such electromagnetic wave.
.. compared with the accuracy of their instruments. In a conductor, the ratio of displacement to conduction current is $\omega\,\epsilon/\sigma$ and this is a fantastically small number at the frequencies experimenters would have probed in Maxwell's day. To get there experimentally was Hertz's big contribution. The unmodified Ampère's law probably explained most experiments, and its inconsistency with the continuity equation was inferred theoretically as described in my other answer. –  WetSavannaAnimal aka Rod Vance Jun 12 at 10:58