14

I do not know how exactly was this picture made, but there are at least two methods. The first one is to compute this potential (which is not too difficult), plot sufficiently many points and connect them by smooth curves. This was still quite common in pre-computer era, in 1970s when a special drawing tool was used, in the shape of a curved ruler of ...


11

Adding to Alexandre's answer. My father, educated in the 1930s, used a set of "French curves" like this Secondly ... perhaps the picture in the post was not drawn by Maxwell himself, but by a professional technical artist.


9

The relation of the speed of light $c$ to electrodynamics was known before Maxwell. In 1846, Weber derived his force law between point charges:1 $$F=\frac{ee'}{r^2}\left[1-\frac{1}{2c^2}\left(\frac{dr}{dt}\right)^2+\frac{1}{c^2}r\frac{d^2r}{dt^2}\right]$$ from Ampère's force law2 (not to be confused with one of Maxwell's equations, the Ampère circuital ...


9

This is a very good question, I wish it got more attention. My answer will only be partial for I had difficulty finding early details on gyromagnetic effect and ratio. The concept comes up every time we have a rotating system of charged particles, because it has angular momentum and creates a magnetic dipole field, and it played an important historical role ...


8

Ampère did. Ampère's force law (not to be confused with one of Maxwell's equations, "Ampère"'s circuital law, which Ampère never wrote down, as Ampère didn't deal with the field concept), written in modern vector notation, gives the force that current elements $I_1 d\vec {\ell }_1$ and $I_2 d\vec {\ell }_2$ exert on one another to be: $$d^2\vec{F_{21}^A} = -...


8

I read somewhere, some time ago that Maxwell originally wrote his eponymous equations using the formalism of quaternions ... Is this true? It seems that the answer is "Not quite". Maxwell originally wrote his equations in components, and later simplified them by using quaternions and some vector calculus. It is true that Heaviside and Gibbs put them into ...


8

For a long time it was not only believed but even ascertained that electric signals moved not just as fast but faster than light, even "instantaneously". The original experiments involving electrostatic discharges of the Leyden jar were made even before wires were introduced. According to Fahie's History of Electric Telegraphy, one of the early experimenters,...


7

"Serious" in the OP sense is probably too high a bar. In 1900-s the situation was very much in flux as to what classical physics could and could not explain. Even Planck's and Einstein's ideas, that we now associate with quantum mechanics, were incorporated into seemingly classical approaches at the time. But what dominated the scene were qualitative ...


7

Maxwell had at least three arguments in favor of the conjecture on electromagnetic nature of light. The first one was philosophical (Chap. XX, section 781). He could not imagine waves propagating in empty space, so for the electromagnetic wave he had to assume the existence of some medium that fills the space. Then he writes: To fill the space with a new ...


7

Of course Maxwell knew Green's theorem, by the time he was writing this was the common knowledge. Maxwell's book has a mathematical preliminary chapter (chapter 2) where he explains mathematical tools he uses, and this contains Gauss, Green, Stokes theorems and much more. (In fact he anticipates what was later called Hodge theory). In the chapter where ...


7

The modern concept of magnetic monopole (as a real isolated charge) is due to Dirac in 1931, although Curie speculated about the possibility earlier. Even electric charges, as in particles, only appeared in 19th century, see Wikipedia's Discovery of two kinds of charges. Before that electricity and magnetism were mostly viewed as produced by fluids, one or ...


6

The micro- in micro-waves, as far as I know, comes from the way that we produced electromagnetic waves at the time: following Hertz, people generally used currents cycling through antennas. Generally for broadcast the antennas would be huge affairs and would radiate in all directions. The radiated wavelength goes proportional to the antenna length because ...


6

Google really is your friend. history.com says E.W. Culgan, a telegraph manager in Pittsburgh, reported that the resulting currents flowing through the wires were so powerful that platinum contacts were in danger of melting and “streams of fire” were pouring forth from the circuits. In Washington, D.C., telegraph operator Frederick W. Royce was ...


6

Newton proved that if the attraction obeys the inverse square law, then the force inside a uniformly charged sphere is zero. It follows from the description that you give that Cavendish used the converse statement. In fact this converse statement is true though I doubt that Cavendish had a proof of it in full generality. It is very common for physicists (...


6

These operations arose from the study of quaternions see e.g. Thomson and Tait's Treatise on Natural Philosophy, that should probably have information on the sort of math. Stokes's theorem originated with Thomson (Lord Kelvin) around 1850 and in there the expression for curl appears. The history of quaternions is certainly interesting, starting with Hamilton ...


5

In order to obtain a nonpulsating power source some early investigators used Wimshurst or similar static electricity generators, or batteries of many small storage cells. (The discovery of the electron, David L. Anderson)


5

"Oliver Heaviside ... what he was doing, why he developed his step function"? A short answer is that Heaviside was interested, as a practical electrical engineer, in transient effects in complex electrical circuits as well as in steady effects. Examples of 'transient' problems: What happens when a switch is flipped (closed), and the circuit is an intricate ...


5

Maxwell did not think of the displacement current as a continuation of the conduction current, and his motivations are generally entwined with his mechanical models of ether. But the naming itself comes from the analogy between the added term and the polarization field induced by electric field in a dielectric, caused by atomic charges slightly separating ...


5

General references on the subject are Whittaker's History of the Theories of Aether and Electricity and Timeline Of History Of Electricity. Newton's persuasive evidence for the inverse square law of gravity was a defining achievent of new science, so of course it invited imitation wherever possible. Newton himself already approaches magnetism with gravity ...


4

This gives the four equations in the form Heaviside came up with: $$\varepsilon E = \rho$$ $$\nabla \times E = - \mu \frac{\partial H}{\partial t}$$ $$\nabla \cdot \mu H = 0$$ $$\nabla \times H = k E + \varepsilon \frac{\partial E}{\partial t}$$ where $E$ represents the electric field, $H$ represents the magnetic field, $\varepsilon$ is the permittivity, $...


4

Yes, they did, and the problem persists in quantum field theory to the extent that electrons can be called "point charges" (they are neither waves nor particles despite common terminology, and technically each one is smeared all over the universe). The classical electron theory of Lorentz-Abraham had multiple issues, some related to electron's point like ...


4

Franz Ernst Neumann was the first¹ to write down the magnetic vector potential in his 1845 paper "General laws of induced electrical currents." He used it to write the equation summarizing Faraday's induction experiment (Faraday's law). The original paper: F. E. Neumann, “Allgemeine Gesetze Der Inducirten Elektrischen Ströme,” Annalen Der Physik 143, no. 1 ...


4

I think the way Millikan deduced the number of electrons was, aside from the current state of knowledge as Conifold relates, by taking lots and lots of measurements (certainly that's what I did when repeating the experiment in undergrad). When you plot the calculated charge on each droplet, you see the points on the graph are not a continuum but rather they ...


4

Heaviside coined the term "permittivity". He explains it and related terms in his Electrical Papers (vol. 2) pp. 124-5, § "Nomenclature Scheme": To explain the word "permittance" that I used in the last Section, I may remark that in stating my views in 1885 in several communications to this journal on the subject of a systematic and convenient electrical ...


4

Benjamin Franklin, with his lightning kite experiment, was one of the first to realize that electricity travels. Ampère knew that parallel wires with current going the same (opposite) direction attract (repel). Thus, if there an AC, you will see the wires vibrating like a plucked string.


4

This was noticed when observations of eclipses of Jupiter satellites deviated from prediction. Before that there could be only speculations (and these speculations existed from antiquity). Jupiter satellites gave the first hard evidence. From the very beginning, Jupiter satellites were proposed by Galileo as a natural clock for determination of longitude. ...


4

I will assume "non-instantaneous" means something other than electric discharge in the atmosphere, from animals like eels and torpedo fishes, or electrostatic generators like the Leyden jar or the van der Graaf generator. Then the answer is the voltaic pile invented by Volta in 1799, "the first electrical battery that could continuously provide an electric ...


4

Subatomic particles, other than electron, photon and proton were not yet discovered in 1925. On the proton (which at the time was only known as hydrogen nucleus "inside" other nuclei), Compton, who conjectured the electron spin in The magnetic electron (1921), wrote: "Besides the molecule and the atom we have the other two fundamental divisions of ...


3

Keep in mind that "intuitions" are personal, 0.999... = 1 may be counterintuitive to you but natural to others, they also strongly depend on historical and cultural context. In 19th century first the wave optics and then Maxwell's electrodynamics strongly suggested existence of a material carrier for light and electromagnetic waves, the ether. Young ...


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