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I am curious about the origin of electric flux and field lines.

-Flux-

I am aware of the fact that flux is a mathematical concept, but how did it find its way into physics? Was it just introduced to replace the E.A in Gauss' Law, or maybe in an attempt to explain inverse square law? Or was it because physicists were experimenting by using all possible operations on vector fields?

-Field lines-

I have a similar doubt regarding regarding field lines. I believe that they were probably introduced to explain the inverse square law by saying that the lines of force get distributed over a surface of a sphere and thus vary inversely with the square of distance. Am I correct?

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    $\begingroup$ No, it is because of the analogy with the velocity field in fluid mechanics, which had already been studied. $\endgroup$ – FGSUZ Oct 12 '18 at 18:22
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    $\begingroup$ I feel this question is better suited for the history of science and mathematics site: hsm.stackexchange.com $\endgroup$ – enumaris Oct 12 '18 at 23:28
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    $\begingroup$ I'm voting to close this question as off-topic because, as @enumaris points out, this seems like more of a question about the history of a physics concept. $\endgroup$ – BioPhysicist Oct 13 '18 at 4:47
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This concept was introduced by probably the greatest experimental physicist, Michael Faraday. He struggled with mathematical concepts so he tried to develop the intuition of magnetic fields using flux and field lines. He was then able to explain various phenomena like electromagnetic induction using this intuition. This concept was shaped mathematically by Maxwell.

Hope this answers your question.

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