Open In Colab

History of Electricity

  • Newton (1660s)
  • Coulomb (1785)
  • Oersted (1819)
  • Ampere (1820--1826)
  • Biot-Savart
  • Faraday (1831), (1851)
  • Weber (1840s+)
  • Maxwell (1860s)

Since working on our PhD thesis (completed November 2019) we have been thinking constantly about history of electrodynamics. But the 19th century discoveries and experiments in electricity remain extremely interesting today (2022). A very rough sketch of the history is something like this: in 1660s Newton presents his law of gravitation. Eventually Coulomb presents a similar law for electric charges, namely the Coulomb force law (1785). Later Oersted (1819) demonstrated that a constant current in a circuit deflects a compass. This experiment was apparently quite shocking to philosophers of the period. Andre-Marie Ampere was so amazed that he began six intensive years of experiment and investigation, eventually publishing his memoir [insert title]. Now Faraday (1831) demonstrated by experiment effects that he called Volta induction. This induction is frequently called "Faraday induction" in contemporary texts. Eventually Faraday (1851) attempted to explain these effects with his field concept. Faraday used many different expressions for the electric and magnetic fluids, for example, but eventually hypothesized the existence of magnetic field lines. Ampere was always opposed to these hypothetical lines, viewing them as ill defined and disposable, i.e. not necessary for any physical explanations.

Later Maxwell (1860s) more formally developed Faraday's field concept into his equations relating $E$ and $B$, namely the so-called electric and magnetic fields. Maxwell also introduced another modification, namely his so-called "displacement current" (Interesting derivation here). But we do not address this further here. Needless to say, it's a strange re-definition of electric current.

Faraday Volta Induction

Eventually we should explain how Wilhelm Weber's force law successfully unifies the laws of Coulomb, Ampere, and Faraday induction. But this is long story. So we begin with the simplest parts.

The basic example of induction is Faraday's experiment, as depicted by Prof. Lewin in the following screenshot. Now notice that the magnetic field is materialized by the circuit $C_1$. It is assumed that a magnetic field $B$ is generated by the circuit $C_1$ when the switch in the circuit is closed. Moreover it's assumed that this switch in the circuit represents a variable magnetic field $\frac{\partial B}{\partial t}$. But again, the magnetic field $B$ is not physical, but rather the circuit $C_1$ is taken implicitly as a proxy representative for the field $B$.

Screenshot_FaradayInduction_Circuit12.jpg

Likewise when Prof. Lewin illustrates how a magnetic field in motion induces a current in a conductor, a bar magnet is necessary as materialization of the otherwise abstract field $B$. We are emphasizing that the magnetic field $B$ is very abstract and immaterial. Yet in all the motivating experiments, the field $B$ is represented by some material object. In the previous set-up this materialization was given by circuit $C_1$. In this example, the materialization is given by the material bar magnet.

Screenshot_FaradayInduction_MagnetMoving.png

Mysteries in the Magnets

Now there remains somewhat a mystery hidden in magnets. Faraday in (1851) introduced the idea of the magnetic field, and this was more formally adopted by Maxwell in his equations (1860s). One of the very important equations is the hypothesis of non-existence of magnetic monopoles. This is the important $$div(B) = \nabla \cdot B = 0$$ law in Maxwell's equations.

However Ampere much earlier in fact discovered the true reason why magnetic monopoles do not exist. Now we cannot go into detail about Assis' proof of the nonexistence of monopoles from Ampere's circuital force law. Indeed when the magnetic field is replaced with the electricthe force of a secondary electric circuit, then $$B=\nabla \times( \oint_C \bf{F} \cdot ds)$$ for a force vector $\bf{F}$ introduced by Ampere [insert reference]. But the trivial algebraic identity $$div(curl)=\nabla \cdot (\nabla ~\times - )=0, $$ and this trivial identity implies the nonexistence of monopoles. This amazing proof is not well-known even in 2022!

Ampere understood that basic North-South magnetic dipoles can be replaced by small current loops. But here is the mystery of magnetism: are magnetic materials filled with small current loops? If these loops have resistance, then this current must eventually dissipate all its energy into heat and die off.

Is it possible for atoms to carry zero-resistance currents?

This is somewhat the mystery left by Ampere. I.e., magnetism remains ultimately unexplained by Ampere, or at least reduced to the above question.

The critics and Maxwellian field view does not offer any better explanation.

What is the physics of the basic magnetic North-South dipole?

They cannot say.

In the conceptual history, we need to appreciate that Oersted's experiment (1819) was a catalyst for investigations into electricity. However the idea of magnetic field was not immediately adopted, especially not by Ampere. In the book [ref] we find the controversies between Ampere and most other scientists about the nature of magnetism and electricity, and the proper interpretatinos of Oersted's experiment. This is somewhat difficult in contemporary research (2022) because the Maxwellian field concepts are deeply implicit in the physicist's mind. But they are not essential, and as Ampere describes, they are disposable hypotheses.