In 1745 a cheap and convenient source of electric sparks was invented by Pieter van Musschenbroek, a physicist and mathematician in Leiden, Netherlands. Later called the Leyden jar, it was the first device that could store large amounts of electric charge. (E. Georg von Kleist, a German cleric, independently developed the idea for such a device but did not investigate it as thoroughly as Musschenbroek did.) The Leyden jar devised by the latter consisted of a glass vial that was partially filled with water and contained a thick conducting wire capable of storing a substantial amount of charge. One end of this wire protruded through the cork that sealed the opening of the vial. The Leyden jar was charged by bringing this exposed end of the conducting wire into contact with a friction device that generated static electricity.

Within a year after the appearance of Musschenbroek’s device, William Watson, an English physician and scientist, constructed a more-sophisticated version of the Leyden jar; he coated the inside and outside of the container with metal foil to improve its capacity to store charge. Watson transmitted an electric spark from his device through a wire strung across the River Thames at Westminster Bridge in 1747.

The Leyden jar revolutionized the study of electrostatics. Soon “electricians” were earning their living all over Europe demonstrating electricity with Leyden jars. Typically, they killed birds and animals with electric shock or sent charges through wires over rivers and lakes. In 1746 the abbé Jean-Antoine Nollet, a physicist who popularized science in France, discharged a Leyden jar in front of King Louis XV by sending current through a chain of 180 Royal Guards. In another demonstration, Nollet used wire made of iron to connect a row of Carthusian monks more than a kilometre long; when a Leyden jar was discharged, the white-robed monks reportedly leapt simultaneously into the air.

In America, Benjamin Franklin sold his printing house, newspaper, and almanac to spend his time conducting electricity experiments. In 1752 Franklin proved that lightning was an example of electric conduction by flying a silk kite during a thunderstorm. He collected electric charge from a cloud by means of wet twine attached to a key and thence to a Leyden jar. He then used the accumulated charge from the lightning to perform electric experiments. Franklin enunciated the law now known as the conservation of charge (the net sum of the charges within an isolated region is always constant). Like Watson, he disagreed with DuFay’s two-fluid theory. Franklin argued that electricity consisted of two states of one fluid, which is present in everything. A substance containing an unusually large amount of the fluid would be “plus,” or positively charged. Matter with less than a normal amount of fluid would be “minus,” or negatively charged. Franklin’s one-fluid theory, which dominated the study of electricity for 100 years, is essentially correct because most currents are the result of moving electrons. At the same time, however, fundamental particles have both negative and positive charges and, in this sense, DuFay’s two-fluid picture is correct.

Joseph Priestley, an English physicist, summarized all available data on electricity in his book History and Present State of Electricity (1767). He repeated one of Franklin’s experiments, in which the latter had dropped small corks into a highly electrified metal container and found that they were neither attracted nor repelled. The lack of any charge on the inside of the container caused Priestley to recall Newton’s law that there is no gravitational force on the inside of a hollow sphere. From this, Priestley inferred that the law of force between electric charges must be the same as the law for gravitational force—i.e., that the force between masses diminishes with the inverse square of the distance between the masses. Although they were expressed in qualitative and descriptive terms, Priestley’s laws are still valid today. Their mathematics was clarified and developed extensively between 1767 and the mid-19th century as electricity and magnetism became precise, quantitative sciences.

Formulation of the quantitative laws of electrostatics and magnetostatics

Charles-Augustin de Coulomb established electricity as a mathematical science during the latter half of the 18th century. He transformed Priestley’s descriptive observations into the basic quantitative laws of electrostatics and magnetostatics. He also developed the mathematical theory of electric force and invented the torsion balance that was to be used in electricity experiments for the next 100 years. Coulomb used the balance to measure the force between magnetic poles and between electric charges at varying distances. In 1785 he announced his quantitative proof that electric and magnetic forces vary, like gravitation, inversely as the square of the distance (see above Fundamentals). Thus, according to Coulomb’s law, if the distance between two charged masses is doubled, the electric force between them is reduced to a fourth. (The English physicist Henry Cavendish, as well as John Robison of Scotland, had made quantitative determinations of this principle before Coulomb, but they had not published their work.)

The mathematicians Siméon-Denis Poisson of France and Carl Friedrich Gauss of Germany extended Coulomb’s work during the 18th and early 19th centuries. Poisson’s equation (published in 1813) and the law of charge conservation contain in two lines virtually all the laws of electrostatics. The theory of magnetostatics, which is the study of steady-state magnetic fields, also was developed from Coulomb’s law. Magnetostatics uses the concept of a magnetic potential analogous to the electric potential (i.e., magnetic poles are postulated with properties analogous to electric charges).

Michael Faraday built upon Priestley’s work and conducted an experiment that verified quite accurately the inverse square law. Faraday’s experiment involving the use of a metal ice pail and a gold-leaf electroscope was the first precise quantitative experiment on electric charge. In Faraday’s time, the gold-leaf electroscope was used to indicate the electric state of a body. This type of apparatus consists of two thin leaves of gold hanging from an insulated metal rod that is mounted inside a metal box. When the rod is charged, the leaves repel each other and the deflection indicates the size of the charge. Faraday began his experiment by charging a metal ball suspended on an insulating silk thread. He then connected the gold-leaf electroscope to a metal ice pail resting on an insulating block and lowered the charged ball into the pail. The electroscope reading increased as the ball was lowered into the pail and reached a steady value once the ball was within the pail. When the ball was withdrawn without touching the pail, the electroscope reading fell to zero. Yet when the ball touched the bottom of the pail, the reading remained at its steady value. On removal the ball was found to be completely discharged. Faraday concluded that the electric charge produced on the outside of the pail, when the ball was inside but not in contact with it, was exactly equal to the initial charge on the ball. He then inserted into the pail other objects, such as a set of concentric pails separated from one another with various insulating materials like sulfur. In each case, the electroscope reading was the same once the ball was completely within the pail. From this Faraday concluded that the total charge of the system was an invariable quantity equal to the initial charge of the ball. The present-day belief that conservation is a fundamental property of charge rests not only on the experiments of Franklin and Faraday but also on its complete agreement with all observations in electric engineering, quantum electrodynamics, and experimental electricity. With Faraday’s work, the theory of electrostatics was complete.