The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understanding and research into the nature of electricity grew throughout the eighteenth and nineteenth centuries through the work of researchers such as André-Marie Ampère, Charles-Augustin de Coulomb, Michael Faraday, Carl Friedrich Gauss and James Clerk Maxwell. In the 19th century it had become clear that electricity and magnetism were related, and their theories were unified: wherever charges are in motion electric current results, and magnetism is due to electric current. The source for electric field is electric charge, whereas that for magnetic field is electric current (charges in motion).
Ancient and classical history The knowledge of static electricity dates back to the earliest civilizations, but for millennia it remained merely an interesting and mystifying phenomenon, without a theory to explain its behavior, and it was often confused with magnetism. The ancients were acquainted with rather curious properties possessed by two minerals, amber (Ancient Greek: ἤλεκτρον, ēlektron) and magnetic iron ore (μαγνῆτις λίθος magnētis lithos, "the Magnesian stone, lodestone"). Amber, when rubbed, attracts lightweight objects, such as feathers; magnetic iron ore has the power of attracting iron.
Based on his find of an Olmec hematite artifact in Central America, the American astronomer John Carlson has suggested that "the Olmec may have discovered and used the geomagnetic lodestone compass earlier than 1000 BC". If true, this "predates the Chinese discovery of the geomagnetic lodestone compass by more than a millennium". Carlson speculates that the Olmecs may have used similar artifacts as a directional device for astrological or geomantic purposes, or to orient their temples, the dwellings of the living or the interments of the dead. The earliest Chinese literature reference to magnetism lies in a 4th-century BC book called The Book of the Devil Valley Master: "When the people of Cheng go out to collect jade, they carry a south-pointer with them so as not to lose their way."
Long before any knowledge of electromagnetism existed, people were aware of the effects of electricity. Lightning and other manifestations of electricity such as St. Elmo's fire were known in ancient times, but it was not understood that these phenomena had a common origin. Ancient Egyptians were aware of shocks when interacting with electric fish (such as the electric catfish) or other animals (such as electric eels). The shocks from animals were apparent to observers since pre-history by a variety of peoples that came into contact with them. Texts from 2750 BC by the ancient Egyptians referred to these fish as "thunderer of the Nile" and saw them as the "protectors" of all the other fish. Another possible approach to the discovery of the identity of lightning and electricity from any other source, is to be attributed to the Arabs, who before the 15th century used the same Arabic word for lightning (barq) and the electric ray. Thales of Miletus, writing at around 600 BC, noted that rubbing fur on various substances such as amber would cause them to attract specks of dust and other light objects. Thales wrote on the effect now known as static electricity. The Greeks noted that if they rubbed the amber for long enough they could even get an electric spark to jump. The ancient Indian medical text Sushruta Samhita describes using magnetic properties of the lodestone to remove arrows embedded in a person's body. These electrostatic phenomena were again reported millennia later by Roman and Arabic naturalists and physicians. Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and electric rays. Pliny in his books writes: "The ancient Tuscans by their learning hold that there are nine gods that send forth lightning and those of eleven sorts." This was in general the early pagan idea of lightning. The ancients held some concept that shocks could travel along conducting objects. Patients with ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them. A group of objects found in Iraq in 1938 dated to the early centuries AD (Sassanid Mesopotamia), called the Baghdad Battery, resembles a galvanic cell and is believed by some to have been used for electroplating. The claims are controversial because of supporting evidence and theories for the uses of the artifacts, physical evidence on the objects conducive for electrical functions, and if they were electrical in nature. Despite, or perhaps as a consequence of this uncertainty, discussing the possible ancient technology may engage young students in the science questions. Magnetic attraction was once accounted for by Aristotle and Thales as the working of a soul in the stone.
Middle Ages and the Renaissance
The magnetic needle compass was developed in the 11th century and it improved the accuracy of navigation by employing the astronomical concept of true north (Dream Pool Essays, 1088). The Chinese scientist Shen Kuo (1031–1095) was the first person known to write about the magnetic needle compass and by the 12th century Chinese were known to use the lodestone compass for navigation. In Europe, the first description of the compass and its use for navigation are of Alexander Neckam (1187), although the use of compasses was already common. Its development, in European history, was due to Flavio Gioja from Amalfi. In the 13th century, Peter Peregrinus, a native of Maricourt in Picardy, conducted experiments on magnetism and wrote the first extant treatise describing the properties of magnets and pivoting compass needles. In 1282, the properties of magnets and dry compasses were discussed by Al-Ashraf Umar II, a Yemeni scholar. The dry compass was invented around 1300 by Italian inventor Flavio Gioja. Magnetism remained elusive to Thomas Aquinas, who in his Summa Theologiae presented it as an example of an "occult"—that is, an unknown—force. Archbishop Eustathius of Thessalonica, Greek scholar and writer of the 12th century, records that Woliver, king of the Goths, was able to draw sparks from his body. The same writer states that a certain philosopher was able while dressing to draw sparks from his clothes, a result seemingly akin to that obtained by Robert Symmer in his silk stocking experiments, a careful account of which may be found in the Philosophical Transactions, 1759. Italian physician Gerolamo Cardano wrote about electricity in De Subtilitate (1550) distinguishing, perhaps for the first time, between electrical and magnetic forces.
17th century Toward the late 16th century, a physician of Queen Elizabeth's time, William Gilbert, in De Magnete, expanded on Cardano's work and invented the Neo-Latin word electrica from ἤλεκτρον (ēlektron), the Greek word for "amber". Gilbert undertook a number of careful electrical experiments, in the course of which he discovered that many substances other than amber, such as sulphur, wax, glass, etc., were capable of manifesting electrical properties. Gilbert also discovered that a heated body lost its electricity and that moisture prevented the electrification of all bodies, due to the now well-known fact that moisture impaired the insulation of such bodies. He also noticed that electrified substances attracted all other substances indiscriminately, whereas a magnet only attracted iron. The many discoveries of this nature earned for Gilbert the title of founder of the electrical science. By investigating the forces on a light metallic needle, balanced on a point, he extended the list of electric bodies, and found also that many substances, including metals and natural magnets, showed no attractive forces when rubbed. He noticed that dry weather with north or east wind was the most favourable atmospheric condition for exhibiting electric phenomena—an observation liable to misconception until the difference between conductor and insulator was understood.
Gilbert's work was followed up by Robert Boyle (1627–1691), the famous natural philosopher who was once described as "father of Chemistry, and uncle of the Earl of Cork." Boyle was one of the founders of the Royal Society when it met privately in Oxford, and became a member of the council after the Society was incorporated by Charles II in 1663. He left a detailed account of his research under the title of Experiments on the Origin of Electricity. He discovered electrified bodies attracted light substances in a vacuum, indicating the electrical effect did not depend upon the air as a medium. He also added resin, and other substances, to the then known list of electrics. In 1663 Otto von Guericke invented a device that is now recognized as an early (possibly the first) electrostatic generator, but he did not recognize it primarily as an electrical device or conduct electrical experiments with it. By the end of the 17th century, researchers had developed practical means of generating electricity by friction with an electrostatic generator, but the development of electrostatic machines did not begin in earnest until the 18th century, when they became fundamental instruments in the studies about the new science of electricity. The first usage of the word electricity is ascribed to Sir Thomas Browne in his 1646 work, Pseudodoxia Epidemica. The first appearance of the term electromagnetism was in Magnes, by the Jesuit luminary Athanasius Kircher, in 1641, which carries the provocative chapter-heading: "Elektro-magnetismos i.e. On the Magnetism of amber, or electrical attractions and their causes" (ἠλεκτρο-μαγνητισμός id est sive De Magnetismo electri, seu electricis attractionibus earumque causis).
18th century
Improving the electric machine
The electric machine was subsequently improved by Francis Hauksbee, his student Litzendorf, and by Prof. Georg Matthias Bose, about 1750. Litzendorf, researching for Christian August Hausen, substituted a glass ball for the sulphur ball of Guericke. Bose was the first to employ the "prime conductor" in such machines, this consisting of an iron rod held in the hand of a person whose body was insulated by standing on a block of resin. Ingenhousz, during 1746, invented electric machines made of plate glass. Experiments with the electric machine were largely aided by the discovery that a glass plate, coated on both sides with tinfoil, would accumulate electric charge when connected with a source of electromotive force. The electric machine was soon further improved by Andrew Gordon, a Scotsman, Professor at Erfurt, who substituted a glass cylinder in place of a glass globe; and by Giessing of Leipzig who added a "rubber" consisting of a cushion of woollen material. The collector, consisting of a series of metal points, was added to the machine by Benjamin Wilson about 1746, and in 1762, John Canton of England (also the inventor of the first pith-ball electroscope in 1754) improved the efficiency of electric machines by sprinkling an amalgam of tin over the surface of the rubber.
Electrics and non-electrics In 1729, Stephen Gray conducted a series of experiments that demonstrated the difference between conductors and non-conductors (insulators), showing amongst other things that a metal wire and even packthread conducted electricity, whereas silk did not. In one of his experiments he sent an electric current through 800 feet of hempen thread which was suspended at intervals by loops of silk thread. When he tried to conduct the same experiment substituting the silk for finely spun brass wire, he found that the electric current was no longer carried throughout the hemp cord, but instead seemed to vanish into the brass wire. From this experiment he classified substances into two categories: "electrics" like glass, resin and silk (what we now call insulators) and "non-electrics" like metal and water (what we now call conductors). "Non-electrics" conducted charges while "electrics" held the charge.
Vitreous and resinous Intrigued by Gray's results, in 1732, C. F. du Fay began to conduct several experiments. In his first experiment, Du Fay concluded that all objects except metals, animals, and liquids could be electrified by rubbing and that metals, animals and liquids could be electrified by means of an electric machine, thus discrediting Gray's "electrics" and "non-electrics" classification of substances. In 1733 Du Fay discovered what he believed to be two kinds of frictional electricity; one generated from rubbing glass, the other from rubbing resin. From this, Du Fay theorized that electricity consists of two electrical fluids, "vitreous" and "resinous", that are separated by friction and that neutralize each other when combined. This picture of electricity was also supported by Christian Gottlieb Kratzenstein in his theoretical and experimental works. The two-fluid theory was later proven wrong and replaced with to the concept of positive and negative electrical charges devised by Benjamin Franklin.
Leyden jar
The Leyden jar, a type of capacitor for electrical energy in large quantities, was invented independently by Ewald Georg von Kleist on 11 October 1744 and by Pieter van Musschenbroek in 1745–1746 at Leiden University (the latter location giving the device its name). William Watson, when experimenting with the Leyden jar, discovered in 1747 that a discharge of static electricity was equivalent to an electric current. Capacitance was first observed by Von Kleist of Leyden in 1754. Von Kleist happened to hold, near his electric machine, a small bottle, in the neck of which there was an iron nail. Touching the iron nail accidentally with his other hand he received a severe electric shock. In much the same way Musschenbroeck assisted by Cunaens received a more severe shock from a somewhat similar glass bottle. Sir William Watson of England greatly improved this device, by covering the bottle, or jar, outside and in with tinfoil. This piece of electrical apparatus will be easily recognized as the well-known Leyden jar, so called by the Abbot Nollet of Paris, after the place of its discovery. In 1741, John Ellicott "proposed to measure the strength of electrification by its power to raise a weight in one scale of a balance while the other was held over the electrified body and pulled to it by its attractive power". As early as 1746, Jean-Antoine Nollet (1700–1770) had performed experiments on the propagation speed of electricity. By involving 200 Carthusian monks connected from hand to hand by iron wires so as to form a circle of about 1.6 km, he was able to prove that this speed is finite, even though very high. In 1749, Sir William Watson conducted numerous experiments to ascertain the velocity of electricity in a wire. These experiments, although perhaps not so intended, also demonstrated the possibility of transmitting signals to a distance by electricity. In these experiments, the signal appeared to travel the 12,276-foot length of the insulated wire instantaneously. Le Monnier in France had previously made somewhat similar experiments, sending shocks through an iron wire 1,319 feet long. About 1750, first experiments in electrotherapy were made. Various experimenters made tests to ascertain the physiological and therapeutical effects of electricity. Typical for this effort was Kratzenstein in Halle who in 1744 wrote a treatise on the subject. Demainbray in Edinburgh examined the effects of electricity upon plants and concluded that the growth of two myrtle trees was quickened by electrification. These myrtles were electrified "during the whole month of October, 1746, and they put forth branches and blossoms sooner than other shrubs of the same kind not electrified." Abbé Ménon in France tried the effects of a continued application of electricity upon men and birds and found that the subjects experimented on lost weight, thus apparently showing that electricity quickened the excretions. The efficacy of electric shocks in cases of paralysis was tested in the county hospital at Shrewsbury, England, with rather poor success.
Late 18th century
Benjamin Franklin promoted his investigations of electricity and theories through the famous, though extremely dangerous, experiment of having his son fly a kite through a storm-threatened sky. A key attached to the kite string sparked and charged a Leyden jar, thus establishing the link between lightning and electricity. Following these experiments, he invented a lightning rod. It is either Franklin (more frequently) or Ebenezer Kinnersley of Philadelphia (less frequently) who is considered to have established the convention of positive and negative electricity. Theories regarding the nature of electricity were quite vague at this period, and those prevalent were more or less conflicting. Franklin considered that electricity was an imponderable fluid pervading everything, and which, in its normal condition, was uniformly distributed in all substances. He assumed that the electrical manifestations obtained by rubbing glass were due to the production of an excess of the electric fluid in that substance and that the manifestations produced by rubbing wax were due to a deficit of the fluid. This explanation was opposed by supporters of the "two-fluid" theory like Robert Symmer in 1759. In this theory, the vitreous and resinous electricities were regarded as imponderable fluids, each fluid being composed of mutually repellent particles while the particles of the opposite electricities are mutually attractive. When the two fluids unite as a result of their attraction for one another, their effect upon external objects is neutralized. The act of rubbing a body decomposes the fluids, one of which remains in excess on the body and manifests itself as vitreous or resinous electricity. Up to the time of Franklin's historic kite experiment, the identity of the electricity developed by rubbing and by electrostatic machines (frictional electricity) with lightning had not been generally established. Dr. Wall, Abbot Nollet, Hauksbee, Stephen Gray and John Henry Winkler had indeed suggested the resemblance between the phenomena of "electricity" and "lightning", Gray having intimated that they only differed in degree. It was doubtless Franklin, however, who first proposed tests to determine the sameness of the phenomena. In a letter to Peter Comlinson of London, on 19 October 1752, Franklin, referring to his kite experiment, wrote,
"At this key the phial (Leyden jar) may be charged; and from the electric fire thus obtained spirits may be kindled, and all the other electric experiments be formed which are usually done by the help of a rubbed glass globe or tube, and thereby the sameness of the electric matter with that of lightning be completely demonstrated." On 10 May 1742 Thomas-François Dalibard, at Marly (near Paris), using a vertical iron rod 40 feet long, obtained results corresponding to those recorded by Franklin and somewhat prior to the date of Franklin's experiment. Franklin's important demonstration of the sameness of frictional electricity and lightning added zest to the efforts of the many experimenters in this field in the last half of the 18th century, to advance the progress of the science. In 1751, Franklin demonstrated the magnetization of sewing needles with electric discharge from a Leyden jar. This connection between electricity and magnetism was suggested to him by a report of a lightning strike in Yorkshire, England in 1731 which damaged a box of knives and forks. When the knives were subsequently placed on top of nails, "the Knives took up the Nails". Henry Elles was one of the first people to suggest links between electricity and magnetism. In 1757 he claimed that he had written to the Royal Society in 1755 about the links between electricity and magnetism, asserting that "there are some things in the power of magnetism very similar to those of electricity" but he did "not by any means think them the same". In 1760 he similarly claimed that in 1750 he had been the first "to think how the electric fire may be the cause of thunder". Among the more important of the electrical research and experiments during this period were those of Franz Aepinus, a noted German scholar (1724–1802) and Henry Cavendish of London, England. Franz Aepinus is credited as the first to conceive of the view of the reciprocal relationship of electricity and magnetism. In his work Tentamen Theoria Electricitatis et Magnetism, published in Saint Petersburg in 1759, he gives the following amplification of Franklin's theory, which in some of its features is measurably in accord with present-day views: "The particles of the electric fluid repel each other, attract and are attracted by the particles of all bodies with a force that decreases in proportion as the distance increases; the electric fluid exists in the pores of bodies; it moves unobstructedly through non-electric (conductors), but moves with difficulty in insulators; the manifestations of electricity are due to the unequal distribution of the fluid in a body, or to the approach of bodies unequally charged with the fluid." Aepinus formulated a corresponding theory of magnetism excepting that, in the case of magnetic phenomena, the fluids only acted on the particles of iron. He also made numerous electrical experiments apparently showing that, in order to manifest electrical effects, tourmaline must be heated to between 37.5 °C and 100 °C. In fact, tourmaline remains unelectrified when its temperature is uniform, but manifests electrical properties when its temperature is rising or falling. Crystals that manifest electrical properties in this way are termed pyroelectric; along with tourmaline, these include sulphate of quinine and quartz. Henry Cavendish independently conceived a theory of electricity nearly akin to that of Aepinus. In 1784, he was perhaps the first to utilize an electric spark to produce an explosion of hydrogen and oxygen in the proper proportions that would create pure water. Cavendish also discovered the inductive capacity of dielectrics (insulators), and, as early as 1778, measured the specific inductive capacity for beeswax and other substances by comparison with an air condenser.
Around 1784 C. A. Coulomb devised the torsion balance, discovering what is now known as Coulomb's law: the force exerted between two small electrified bodies varies inversely as the square of the distance, not as Aepinus in his theory of electricity had assumed, merely inversely as the distance. According to the theory advanced by Cavendish, "the particles attract and are attracted inversely as some less power of the distance than the cube." A large part of the domain of electricity became virtually annexed by Coulomb's discovery of the law of inverse squares. Through the experiments of William Watson and others proving that electricity could be transmitted to a distance, the idea of making practical use of this phenomenon began, around 1753, to engross the minds of inquisitive people. To this end, suggestions as to the employment of electricity in the transmission of intelligence were made. The first of the methods devised for this purpose was probably that of Georges Lesage in 1774. This method consisted of 24 wires, insulated from one another and each having had a pith ball connected to its distant end. Each wire represented a letter of the alphabet. To send a message, a desired wire was charged momentarily with electricity from an electric machine, whereupon the pith ball connected to that wire would fly out. Other methods of telegraphing in which frictional electricity was employed were also tried, some of which are described in the history on the telegraph. The era of galvanic or voltaic electricity represented a revolutionary break from the historical focus on frictional electricity. Alessandro Volta discovered that chemical reactions could be used to create positively charged anodes and negatively charged cathodes. When a conductor was attached between these, the difference in the electrical potential (also known as voltage) drove a current between them through the conductor. The potential difference between two points is measured in units of volts in recognition of Volta's work. The first mention of voltaic electricity, although not recognized as such at the time, was probably made by Johann Georg Sulzer in 1767, who, upon placing a small disc of zinc under his tongue and a small disc of copper over it, observed a peculiar taste when the respective metals touched at their edges. Sulzer assumed that when the metals came together they were set into vibration, acting upon the nerves of the tongue to produce the effects noticed. In 1790, Prof. Luigi Alyisio Galvani of Bologna, while conducting experiments on "animal electricity", noticed the twitching of a frog's legs in the presence of an electric machine. He observed that a frog's muscle, suspended on an iron balustrade by a copper hook passing through its dorsal column, underwent lively convulsions without any extraneous cause, the electric machine being at this time absent. To account for this phenomenon, Galvani assumed that electricity of opposite kinds existed in the nerves and muscles of the frog, the muscles and nerves constituting the charged coatings of a Leyden jar. Galvani published the results of his discoveries, together with his hypothesis, which engrossed the attention of the physicists of that time. The most prominent of these was Volta, professor of physics at Pavia, who contended that the results observed by Galvani were the result of the two metals, copper and iron, acting as electromotors, and that the muscles of the frog played the part of a conductor, completing the circuit. This precipitated a long discussion between the adherents of the conflicting views. One group agreed with Volta that the electric current was the result of an electromotive force of contact at the two metals; the other adopted a modification of Galvani's view and asserted that the current was the result of a chemical affinity between the metals and the acids in the pile. Michael Faraday wrote in the preface to his Experimental Researches, relative to the question of whether metallic contact is productive of a part of the electricity of the voltaic pile: "I see no reason as yet to alter the opinion I have given; ... but the point itself is of such great importance that I intend at the first opportunity renewing the inquiry, and, if I can, rendering the proofs either on the one side or the other, undeniable to all." Even Faraday himself, however, did not settle the controversy, and while the views of the advocates on both sides of the question have undergone modifications, as subsequent investigations and discoveries demanded, up to 1918 diversity of opinion on these points continued to crop out. Volta made numerous experiments in support of his theory and ultimately developed the pile or battery, which was the precursor of all subsequent chemical batteries, and possessed the distinguishing merit of being the first means by which a prolonged continuous current of electricity was obtainable. Volta communicated a description of his pile to the Royal Society of London and shortly thereafter Nicholson and Cavendish (1780) produced the decomposition of water by means of the electric current, using Volta's pile as the source of electromotive force.
19th century
Early 19th century
In 1800 Alessandro Volta constructed the first device to produce a large electric current, later known as the electric battery. Napoleon, informed of his works, summoned him in 1801 for a command performance of his experiments. He received many medals and decorations, including the Légion d'honneur. Davy in 1806, employing a voltaic pile of approximately 250 cells, or couples, decomposed potash and soda, showing that these substances were respectively the oxides of potassium and sodium, metals which previously had been unknown. These experiments were the beginning of electrochemistry, the investigation of which Faraday took up, and concerning which in 1833 he announced his important law of electrochemical equivalents, viz.: "The same quantity of electricity — that is, the same electric current — decomposes chemically equivalent quantities of all the bodies which it traverses; hence the weights of elements separated in these electrolytes are to each other as their chemical equivalents." Employing a battery of 2,000 elements of a voltaic pile Humphry Davy in 1809 gave the first public demonstration of the electric arc light, using charcoal enclosed in a vacuum. Somewhat important to note, it was not until many years after the discovery of the voltaic pile that the sameness of animal and frictional electricity with voltaic electricity was clearly recognized and demonstrated. Thus as late as January 1833 we find Faraday writing in a paper on the electricity of the electric ray. "After an examination of the experiments of Walsh, Ingenhousz, Henry Cavendish, Sir H. Davy, and Dr. Davy, no doubt remains on my mind as to the identity of the electricity of the torpedo with common (frictional) and voltaic electricity; and I presume that so little will remain on the mind of others as to justify my refraining from entering at length into the philosophical proof of that identity. The doubts raised by Sir Humphry Davy have been removed by his brother, Dr. Davy; the results of the latter being the reverse of those of the former. ... The general conclusion which must, I think, be drawn from this collection of facts (a table showing the similarity, of properties of the diversely named electricities) is, that electricity, whatever may be its source, is identical in its nature." It is proper to state, however, that prior to Faraday's time the similarity of electricity derived from different sources was more than suspected. Thus, William Hyde Wollaston, wrote in 1801: "This similarity in the means by which both electricity and galvanism (voltaic electricity) appear to be excited in addition to the resemblance that has been traced between their effects shows that they are both essentially the same and confirm an opinion that has already been advanced by others, that all the differences discoverable in the effects of the latter may be owing to its being less intense, but produced in much larger quantity." In the same paper Wollaston describes certain experiments in which he uses very fine wire in a solution of sulphate of copper through which he passed electric currents from an electric machine. This is interesting in connection with the later day use of almost similarly arranged fine wires in electrolytic receivers in wireless, or radio-telegraphy.
In the first half of the 19th century many very important additions were made to the world's knowledge concerning electricity and magnetism. For example, in 1820 Hans Christian Ørsted of Copenhagen discovered the deflecting effect of an electric current traversing a wire upon a suspended magnetic needle. This discovery gave a clue to the subsequently proved intimate relationship between electricity and magnetism which was promptly followed up by Ampère who some months later, in September 1820, presented the first elements of his new theory, which he developed in the following years culminating with the publication in his 1827 "Mémoire sur la théorie mathématique des phénomènes électrodynamiques uniquement déduite de l’experience" (Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience) announcing his celebrated theory of electrodynamics, relating to the force that one current exerts upon another, by its electro-magnetic effects, namely
Two parallel portions of a circuit attract one another if the currents in them are flowing in the same direction, and repel one another if the currents flow in the opposite direction. Two portions of circuits crossing one another obliquely attract one another if both the currents flow either towards or from the point of crossing, and repel one another if one flows to and the other from that point. When an element of a circuit exerts a force on another element of a circuit, that force always tends to urge the second one in a direction at right angles to its own direction.
Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. James Clerk Maxwell, in his "A Treatise on Electricity and Magnetism", named Ampere “the Newton of electricity”. The German physicist Seebeck discovered in 1821 that when heat is applied to the junction of two metals that had been soldered together an electric current is set up. This is termed thermoelectricity. Seebeck's device consists of a strip of copper bent at each end and soldered to a plate of bismuth. A magnetic needle is placed parallel with the copper strip. When the heat of a lamp is applied to the junction of the copper and bismuth an electric current is set up which deflects the needle. Around this time, Siméon Denis Poisson attacked the difficult problem of induced magnetization, and his results, though differently expressed, are still the theory, as a most important first approximation. It was in the application of mathematics to physics that his services to science were performed. Perhaps the most original, and certainly the most permanent in their influence, were his memoirs on the theory of electricity and magnetism, which virtually created a new branch of mathematical physics. George Green wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism in 1828. The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. George Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as James Clerk Maxwell, William Thomson, and others. Peltier in 1834 discovered an effect opposite to thermoelectricity, namely, that when a current is passed through a couple of dissimilar metals the temperature is lowered or raised at the junction of the metals, depending on the direction of the current. This is termed the Peltier effect. The variations of temperature are found to be proportional to the strength of the current and not to the square of the strength of the current as in the case of heat due to the ordinary resistance of a conductor. This second law is the I2R law, discovered experimentally in 1841 by the English physicist Joule. In other words, this important law is that the heat generated in any part of an electric circuit is directly proportional to the product of the resistance R of this part of the circuit and to the square of the strength of current I flowing in the circuit. In 1822 Johann Schweigger devised the first galvanometer. This instrument was subsequently much improved by Wilhelm Weber (1833). In 1825 William Sturgeon of Woolwich, England, invented the horseshoe and straight bar electromagnet, receiving therefor the silver medal of the Society of Arts. In 1837 Carl Friedrich Gauss and Weber (both noted workers of this period) jointly invented a reflecting galvanometer for telegraph purposes. This was the forerunner of the Thomson reflecting and other exceedingly sensitive galvanometers once used in submarine signaling and still widely employed in electrical measurements. Arago in 1824 made the important discovery that when a copper disc is rotated in its own plane, and if a magnetic needle be freely suspended on a pivot over the disc, the needle will rotate with the disc. If on the other hand the needle is fixed it will tend to retard the motion of the disc. This effect was termed Arago's rotations.
Futile attempts were made by Charles Babbage, Peter Barlow, John Herschel and others to explain this phenomenon. The true explanation was reserved for Faraday, namely, that electric currents are induced in the copper disc by the cutting of the magnetic lines of force of the needle, which currents in turn react on the needle. Georg Simon Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet. He drew considerable inspiration from Fourier's work on heat conduction in the theoretical explanation of his work. For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant potential difference. He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through a simple equation with variable composed of the reading from a galvanometer, the length of the test conductor, thermocouple junction temperature, and a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results. In 1827, he announced the now famous law that bears his name, that is:
Ohm brought into order a host of puzzling facts connecting electromotive force and electric current in conductors, which all previous electricians had only succeeded in loosely binding together qualitatively under some rather vague statements. Ohm found that the results could be summed up in such a simple law and by Ohm's discovery a large part of the domain of electricity became annexed to theory.
Faraday and Henry
The discovery of electromagnetic induction was made almost simultaneously, although independently, by Michael Faraday, who was first to make the discovery in 1831, and Joseph Henry in 1832. Henry's discovery of self-induction and his work on spiral conductors using a copper coil were made public in 1835, just before those of Faraday. In 1831 began the epoch-making researches of Michael Faraday, the famous pupil and successor of Humphry Davy at the head of the Royal Institution, London, relating to electric and electromagnetic induction. The remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Faraday was not a competent mathematician, but had he been one, he would have been greatly assisted in his researches, have saved himself much useless speculation, and would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann's theory, and the connected work of Helmholtz and Thomson. Faraday's studies and researches extended from 1831 to 1855 and a detailed description of his experiments, deductions and speculations are to be found in his compiled papers, entitled Experimental Researches in Electricity.' Faraday was by profession a chemist. He was not in the remotest degree a mathematician in the ordinary sense — indeed it is a question if in all his writings there is a single mathematical formula.
The experiment which led Faraday to the discovery of electromagnetic induction was made as follows: He constructed what is now and was then termed an induction coil, the primary and secondary wires of which were wound on a wooden bobbin, side by side, and ins