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Ampère, a half century before Maxwell, theorized that magnetism was caused by electrical currents. So, why is Maxwell and not Ampère credited for unifying electricity and magnetism?

(cf. the question "Why is one of Maxwell's equations named after Ampère?")

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    $\begingroup$ Because Maxwell improved the equations of Ampere, and made them consistent with Faraday's &tc. Maxwell's equations completed the unification begun with Oersted's discovery. $\endgroup$ – Peter Diehr Jul 28 '16 at 21:52
  • $\begingroup$ @PeterDiehr How weren't "the equations of Ampere" (do you mean his force law?) of Ampère inconsistent with Faraday? $\endgroup$ – Geremia Jul 29 '16 at 23:03
  • $\begingroup$ have you studied Maxwell's equations in detail? Are you familiar with how Maxwell altered Ampere's equation, and why? This site provides a nice review of the physics, history, and some of the math: maxwells-equations.com $\endgroup$ – Peter Diehr Jul 30 '16 at 0:59
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    $\begingroup$ @PeterDiehr That site says: "Maxwell…took a set of known experimental laws (Faraday's Law, Ampere's Law) and unified them into a symmetric coherent set of Equations known as Maxwell's Equations." I think by "Ampere's Law" he means the Maxwell equation involving current ("Ampère circuital law," sometimes called, more properly, the Ampère-Maxwell equation, named after Ampère because of his studies of electric current), not Ampère's force law. $\endgroup$ – Geremia Jul 30 '16 at 5:00
  • $\begingroup$ @PeterDiehr Thus, implicit in my question here is the fact that there is a discontinuity between Ampère's and Maxwell's work. $\endgroup$ – Geremia Jul 30 '16 at 5:03
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On my opinion, the following citation from Poincare answers this question:

“At the time, when Maxwell initiated his studies, the laws of electrodynamics adopted before him explained all known phenomena. He started his work not because some new experiment limited the importance of these laws. But, considering them from a new standpoint, Maxwell noticed that the equations became more symmetric, when a certain term was introduced into them, although, on the other hand, this term was too small to give rise to phenomena, that could be estimated by the previous methods. A priori ideas of Maxwell are known to have waited for their experimental confirmation for twenty years; if you prefer another expression, — Maxwell anticipated the experiment by twenty years". (H. Poincare, The value of Science).

Maxwell's contribution was introduction of the so-called "displacement current". Then his equations predicted the existence of electromagnetic waves, the thing experimentally confirmed by Hertz.

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  • $\begingroup$ As I mention in my comment above, Kohlrausch & Weber in 1856 were the first to discover that electromagnetic waves propagate at the speed of light in vacuum. The English translation of their paper is: "On the amount of electricity which flows through the cross-section of the circuit in galvanic currents" (see the appendix for the translation). Was Hertz the first to experimentally demonstrate the propagation of EM waves in free space? $\endgroup$ – Geremia Aug 6 '16 at 22:30
  • $\begingroup$ @Geremia: as far as I know Hertz was the first to demonstrate the existence of e-m waves. Did K&W have the correct Maxwell equations? $\endgroup$ – Alexandre Eremenko Aug 9 '16 at 20:03
  • $\begingroup$ No, they didn't have anything like Maxwell's equation with displacement current. Kirchhoff and Weber in 1857, independently of each other, discovered the wave equation for the propagation of electromagnetic signals in a wire. I think Hertz was indeed the first to discover the propagation of electromagnetic signals in vacuo, though. $\endgroup$ – Geremia Aug 9 '16 at 23:19
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    $\begingroup$ @Geremia: It follows that Maxwell is rightly credited for the complete set of Maxwell's equations. $\endgroup$ – Alexandre Eremenko Aug 15 '16 at 18:07
  • $\begingroup$ Maxwell's unique contribution was his "Ampère's" circuital law (both forms: with and without the displacement current term). Faraday's Law was derived by Franz Neumann in 1845. Gauss (and Lagrange before him) knew the compatibility between Coulomb's law and "Gauss"'s law. I'm not sure who was the first to derive $\nabla\cdot\mathbf{B}=0$. $\endgroup$ – Geremia Aug 16 '16 at 18:11
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There are two reasons:

  • As explained by Alexandre Eremenko, the laws of electrodynamics before Maxwell (like Ampere's force law, Neumann's law of induction, Weber's law, etc.) explained all the known phenomena in an action at a distance manner. When action at a distance theories fell out of favour, the pioneers of these theories were mostly discredited. Not to mention the fact that these pioneers had their name attached to some part of field theory. For eg $-$ Ampere's circuital law, Gauss law, etc.

  • In the later accepted field theory, the pioneer was James Clerk Maxwell (Faraday did initiated field theory but it was Maxwell who mathematically expressed them). Not only he expressed them mathematically but also symmetrically.

From these two reasons it would be obvious that it was only Maxwell who would be eligible for being credited as "unifier of electricity and magnetism"

Here is a quote from Maxwell's treatise regarding field theory vs action at a distance theory:

In a philosophical point of view, moreover, it is exceedingly important that two methods should be compared, both of which have succeeded in explaining the principal electromagnetic phenomena, and both of which have attempted to explain the propagation of light as an electromagnetic phenomenon, and have actually calculated its velocity, while at the same time the fundamental conceptions of what actually takes place, as well as most of the secondary conceptions of the quantities concerned, are radically different. I have therefore taken the part of an advocate rather than that of a judge, and have rather exemplified one method than attempted to give an impartial description of both. I have no doubt that the method which I have called the German one (action at a distance) will also find its supporters, and will be expounded with a skill worthy of its ingenuity.

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  • $\begingroup$ @Geremia: If possible, can you give your e-mail so that we can discuss these in length over there. $\endgroup$ – Joe Jan 3 '18 at 8:08
  • $\begingroup$ "the laws of electrodynamics before Maxwell…explained all the known phenomena in an action at a distance manner." But Weber's law, for example, depends upon the speed of light $c$. $\endgroup$ – Geremia Jan 3 '18 at 19:02
  • $\begingroup$ See my profile for my Tox ID; that's the best way to get in touch. $\endgroup$ – Geremia Jan 3 '18 at 19:03
  • $\begingroup$ Yes.... Weber's force law was action at a distance and also contained a constant $c$ which came out to be equal to the speed of light.... So what? $\endgroup$ – Joe Jan 4 '18 at 4:55

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