# Part I: Electricity

For two and a half millennia the fields of electricity and magnetism were separate and distinct. This all changed in 1820, when Hans Christian Ørsted discovered electromagnetism. However, in order to observe an electric current deflect a compass needle, Ørsted must have had access to a powerful battery of electrochemical cells. For someone to build a powerful battery, someone else had to invent the electrochemical cell, which required access to electrical wires and knowledge of conductivity. Thus, knowledge begets knowledge, and that is how science progresses over time.

This positivist view of the history of science predicts that the rate of knowledge increases in proportion to the existing knowledge. The more we know the faster we learn, so we would expect an exponential increase in knowledge over time. For example, let K be the amount of knowledge. If $\tfrac{\text{d}}{\text{d}t}K\propto K,$ then by separation of variables $K={{K}_{0}}{{e}^{\left( t-{{t}_{0}} \right)/\tau }}={{K}_{0}}{{2}^{\left( t-{{t}_{0}} \right)/{{\tau }_{2}}}},$ where ${{K}_{0}}$ represents the amount of knowledge at time ${{t}_{0}},$ and ${{\tau }_{2}}$ represents the doubling time. For example, the modern American chemist, electrical engineer, and entrepreneur, Gordon Moore , predicted that the number of transistors per microchip, at fixed area and cost, would double every two years.[1] If we quantify knowledge of electricity as Moore did, it has increased exponentially for over half a century. Moore’s law is somewhat unique, as it became the driving goal of the microchip industry, so one could argue that it became its own cause‑a self-fulfilling prophecy[2]. Regardless of the details, the conceptual idea that knowledge begets knowledge is firmly etched in our scientific mythos.

If any field of science actually followed this cartoon history, it was electricity. For the past 2500 years, the Western understanding of electricity progressed in a monotonically increasing manner from Thales’s discovery of static electricity to Moore’s law today. This is likely because, as opposed to many other fields[3], physicists mostly got electrical theory right the first time around.

We begin our book with the work of an Englishman, although he later revolted against his king. This experimentalist not only developed the most precisely verified law in all of physics, the conservation of charge, but developed a framework for understanding electricity as a fluid of particles that we still use today. Or, in his words:

The electrical matter consists of particles extremely subtle, since it can permeate common matter, even the densest metals, with such ease and freedom as not to receive any perceptible resistance.[4]

Thus, with the work of Benjamin Franklin, the fluid model of electricity was born. (The picture on the top of this page is Franklin’s.)

Over time, Franklin’s attention turned from physics to politics, which eventually led him to Paris to persuade the French to declare war on Britain. While there, Franklin met a scientist named Charles-Augustin de Coulomb . Soon afterwards, Coulomb measured the force law between charged objects, which is the topic of our second chapter.

Meanwhile in Italy, Alessandro Volta showed that a pile of electrodes, made of different metals soaked in salt water, causes charge to flow. This invention, then, led to whole batteries of these voltaic cells, which, when placed in series or parallel, could produce steady electrical current that could we used for further study. This, in turn, allowed Ørsted to pass a steady current near a magnetized compass needle.

In the hands of the top European mathematicians, Franklin’s ideas and Coulomb’s law, turned into a complete theory of electrical charge, electrical forces, and electrical potential energy. This is the topic of our first 5 chapters.

[1] G.E. Moore, Cramming More Components onto Integrated Circuits, Electronics, April 19, 1965, pp. 114-117.

[2] Had Moore not come up with his law, the speed of computers probably would have still increased pretty much exponentially, but not spot on as it has for the past 50 years.

[3] This contrasted sharply with the history of both magnetism and optics, as we will discuss in the introductions to Parts II and III (pp. 255 and 521 respectively).

[4] Benjamin Franklin, “Opinions and Conjectures, Concerning the Properties and Effects of the Electrical Matter, etc.,” letter to Peter Collinson, July 29, 1750, reprinted in The Papers of Benjamin Franklin, vol. 4 (Yale University Press, 1961), p. 9. See also, B. Franklin, Experiments and Observations on Electricity, illustrated by I. Hulett, 5th Ed., (London: F. Newberry at the Corner of St. Paul’s Church-Yard, 1774), p. 54.