$$\oint B.dl = \mu_0\left(I+\epsilon_0\frac{\partial\Phi_E}{\partial t}\right)$$ 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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$\begingroup$ '+1' to counter the silent downvotes. $\endgroup$– user31782Commented Jun 12, 2014 at 10:17
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$\begingroup$ @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 :) $\endgroup$– Selene RoutleyCommented Jun 12, 2014 at 11:23
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1$\begingroup$ @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. $\endgroup$– garypCommented Jun 12, 2014 at 12:30
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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.
Historians of physics widely consider that Maxwell's foretelling was first vindicated by the Hertz Spark Gap experiment.
So, without being too glib, the great J C Maxwell's main gig was the second term on the right hand side of your equation.
answered Jun 12, 2014 at 10:14
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$\begingroup$ Well, I am aquainted with that good. But is that all? $\endgroup$– RohitCommented Jun 12, 2014 at 10:24
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$\begingroup$ I mean, this was the implication, but were thete any other direct hand applications of the circuital law $\endgroup$– RohitCommented Jun 12, 2014 at 10:25
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$\begingroup$ Well I should think what I wrote answered what you asked: if this was wonted you already, this was not apparent in your question. Applications of the modified Ampère law? EM waves ARE the main application: wireless communications, radar, radio astronomy, the grounding for the quantum description of light (in which Maxwell's equations still play a big role and are the wave equation for the lone photon) and so on and so forth. As for applications at the time, I'm not sure. I'm guessing that they would have been rather few, for the displacement current was, numerically, a subtle thing .... $\endgroup$ Commented Jun 12, 2014 at 10:56
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$\begingroup$ .. 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. $\endgroup$ Commented Jun 12, 2014 at 10:58