MICHAEL FARADAY Biography - Theater, Opera and Movie personalities

 
 

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MICHAEL FARADAY
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English physicist and chemist whose many experiments contributed greatly to the understanding of electromagnetism. Faraday, who became one of the greatest scientists of the 19th century, began his career as a chemist. Many consider him the greatest experimentalist who ever lived. Several concepts that he derived directly from experiments, such as lines of magnetic force, have become common ideas in modern physics.

       

He wrote a manual of practical chemistry that reveals his mastery of the technical aspects of his art, discovered a number of new organic compounds, among them benzene, and was the first to liquefy a “permanent” gas (i.e., one that was believed to be incapable of liquefaction). His major contribution, however, was in the field of electricity and magnetism.

       

He was the first to produce an electric current from a magnetic field, invented the first electric motor and dynamo, demonstrated the relation between electricity and chemical bonding, discovered the effect of magnetism on light, and discovered and named diamagnetism, the peculiar behaviour of certain substances in strong magnetic fields. He provided the experimental, and a good deal of the theoretical, foundation upon which James Clerk Maxwell erected classical electromagnetic field theory.

       

He introduced several words that we still use today to discuss electricity: ion, electrode, cathode, and anode. Early life: Michael Faraday was born on Sept. 22, 1791 in a poor and very religious family in the country village of Newington, Surrey, now a part of South London. His father was a blacksmith who had migrated from the north of England earlier in 1791 to look for work. His mother was a country woman of great calm and wisdom who supported her son emotionally through a difficult childhood.

       

Faraday was one of four children, all of whom were hard put to get enough to eat, since their father was often ill and incapable of working steadily. Faraday later recalled being given one loaf of bread that had to last him for a week. The family belonged to a small Christian sect, called Sandemanians, that provided spiritual sustenance to Faraday throughout his life.

       

It was the single most important influence upon him and strongly affected the way in which he approached and interpreted nature. Faraday himself, shortly after his marriage, at the age of thirty, joined the same sect, to which he adhered till his death. Religion and science he kept strictly apart, believing that the data of science were of an entirely different nature from the direct communications between God and the soul on which his religious faith was based.

       

Faraday received only the rudiments of an education, learning to read, write, and cipher in a church Sunday school. At an early age he began to earn money by delivering newspapers for a book dealer and bookbinder, and at the age of 14 he was apprenticed to the man. Unlike the other apprentices, Faraday took the opportunity to read some of the books brought in for rebinding. The article on electricity in the third edition of the Encyclopadia Britannica particularly fascinated him. Using old bottles and lumber, he made a crude electrostatic generator and did simple experiments. He also built a weak voltaic pile with which he performed experiments in electrochemistry.

       

He was also among other young Londoners who persued an interest in science by gathering to hear talks at the City Philosophical Society. Faraday’s great opportunity came when he was offered a free ticket to attend chemical lectures by Sir Humphry Davy at the Royal Institution of Great Britain in London. Faraday went, sat absorbed with it all, recorded the lectures in his notes, and returned to bookbinding with the seemingly unrealizable hope of entering the temple of science.

       

He sent a bound copy of his notes to Davy along with a letter asking for employment, but there was no opening. Davy did not forget, however, and, when one of his laboratory assistants was dismissed for brawling, he offered Faraday a job. His first assignment was to accompany Sir Humphry and his wife on a tour of the Continent, during which he sometimes had to be a personal servant to Lady Davy. Then Faraday began as Davy’s laboratory assistant and learned chemistry at the elbow of one of the greatest practitioners of the day. It has been said, with some truth, that Faraday was Davy’s greatest discovery.

       

When Faraday joined Davy in 1812, Davy was in the process of revolutionizing the chemistry of the day. Antoine-Laurent Lavoisier, the Frenchman generally credited with founding modern chemistry, had effected his rearrangement of chemical knowledge in the 1770s and 1780s by insisting upon a few simple principles. Among these was that oxygen was a unique element, in that it was the only supporter of combustion and was also the element that lay at the basis of all acids. Davy, after having discovered sodium and potassium by using a powerful current from a galvanic battery to decompose oxides of these elements, turned to the decomposition of muriatic (hydrochloric) acid, one of the strongest acids known.

       

The products of the decomposition were hydrogen and a green gas that supported combustion and that, when combined with water, produced an acid. Davy concluded that this gas was an element, to which he gave the name chlorine, and that there was no oxygen whatsoever in muriatic acid. Acidity, therefore, was not the result of the presence of an acid-forming element but of some other condition. What else could that condition be but the physical form of the acid molecule itself? Davy suggested, then, that chemical properties were determined not by specific elements alone but also by the ways in which these elements were arranged in molecules. In arriving at this view he was influenced by an atomic theory that was also to have important consequences for Faraday’s thought.

       

This theory, proposed in the 18th century by Ruggero Giuseppe Boscovich, argued that atoms were mathematical points surrounded by alternating fields of attractive and repulsive forces. A true element comprised a single such point, and chemical elements were composed of a number of such points, about which the resultant force fields could be quite complicated. Molecules, in turn, were built up of these elements, and the chemical qualities of both elements and compounds were the results of the final patterns of force surrounding clumps of point atoms. One property of such atoms and molecules should be specifically noted: they can be placed under considerable strain, or tension, before the “bonds” holding them together are broken. These strains were to be central to Faraday’s ideas about electricity.

       

Faraday’s second apprenticeship, under Davy, came to an end in 1820. By then he had learned chemistry as thoroughly as anyone alive. He had also had ample opportunity to practice chemical analyses and laboratory techniques to the point of complete mastery, and he had developed his theoretical views to the point that they could guide him in his researches. There followed a series of discoveries that astonished the scientific world.

       

Michael Faraday

       

Engraving after an original work by Charles Turner (1773-1857)
Faraday achieved his early renown as a chemist. As his chemical capabilities increased, he was given more responsibility. In 1825 he replaced the seriously ailing Davy in his duties directing the laboratory at the Royal Institution. In 1833 he was appointed to the Fullerian Professorship of Chemistry-a special research chair created for him. His reputation as an analytical chemist led to his being called as an expert witness in legal trials and to the building up of a clientele whose fees helped to support the Royal Institution.

       

In 1820 he produced the first known compounds of carbon and chlorine, C2Cl6 and C2Cl4. These compounds were produced by substituting chlorine for hydrogen in “olefiant gas” (ethylene), the first substitution reactions induced. (Such reactions later would serve to challenge the dominant theory of chemical combination proposed by Jons Jacob Berzelius.) In 1825, as a result of research on illuminating gases, Faraday isolated and described benzene.

       

In the 1820s he also conducted investigations of steel alloys, helping to lay the foundations for scientific metallurgy and metallography. While completing an assignment from the Royal Society of London to improve the quality of optical glass for telescopes, he produced a glass of very high refractive index that was to lead him, in 1845, to the discovery of diamagnetism.

       

In 1821 he married Sarah Barnard, settled permanently at the Royal Institution, and began the series of researches on electricity and magnetism that was to revolutionize physics.

       

Faraday announcing his discovery to his wife on Christmas morning, 1821 (from “Electricity in Daily Life", C.F. Brackett et al., 1890)

       

Michael Faraday with his wife Sarah

       

Faraday’s research into electricity and electrolysis was guided by the belief that electricity is only one of the many manifestations of the unified forces of nature, which included heat, light, magnetism, and chemical affinity. Although this idea was erroneous, it led him into the field of electromagnetism, which was still in its infancy. In 1785, Charles Coulomb had been the first to demonstrate the manner in which electric charges repel one another, and it was not until 1820 that Hans Christian Oersted and Andre Marie Ampere discovered that an electric current produces a magnetic field.

       

Faraday’s ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a magnetic field should be able to produce an electric current. He demonstrated this principle of induction in 1831. Faraday expressed the electric current induced in the wire in terms of the number of lines of force that are cut by the wire. The principle of induction was a landmark in applied science, for it made possible the dynamo, or generator, which produces electricity by mechanical means.

       

Faraday’s introduction of the concept of lines of force was rejected by most of the mathematical physicists of Europe, since they assumed that electric charges attract and repel one another, by action at a distance, making such lines unnecessary. Faraday had demonstrated the phenomenon of electromagnetism in a series of experiments, however. Faraday’s descriptive theory of lines of force moving between bodies with electrical and magnetic properties enabled James Clerk Maxwell to formulate an exact mathematical theory of the propagation of electromagnetic waves.

       

In 1865, Maxwell proved mathematically that electromagnetic phenomena are propagated as waves through space with the velocity of light, thereby laying the foundation of radio communication confirmed experimentally in 1888 by Hertz and developed for practical use by Guglielmo Marconi at the turn of the century.

       

In 1820 Hans Christian Orsted had announced the discovery that the flow of an electric current through a wire produced a magnetic field around the wire. Andre-Marie Ampere showed that the magnetic force apparently was a circular one, producing in effect a cylinder of magnetism around the wire. No such circular force had ever before been observed, and Faraday was the first to understand what it implied. If a magnetic pole could be isolated, it ought to move constantly in a circle around a current-carrying wire. Faraday’s ingenuity and laboratory skill enabled him to construct an apparatus that confirmed this conclusion. This device, which transformed electrical energy into mechanical energy, was the first electric motor.

       

This discovery led Faraday to contemplate the nature of electricity. Unlike his contemporaries, he was not convinced that electricity was a material fluid that flowed through wires like water through a pipe. Instead, he thought of it as a vibration or force that was somehow transmitted as the result of tensions created in the conductor. One of his first experiments after his discovery of electromagnetic rotation was to pass a ray of polarized light through a solution in which electrochemical decomposition was taking place in order to detect the intermolecular strains that he thought must be produced by the passage of an electric current. During the 1820s he kept coming back to this idea, but always without result.

       

In the spring of 1831 Faraday began to work with Charles (later Sir Charles) Wheatstone on the theory of sound, another vibrational phenomenon. He was particularly fascinated by the patterns (known as Chladni figures) formed in light powder spread on iron plates when these plates were thrown into vibration by a violin bow. Here was demonstrated the ability of a dynamic cause to create a static effect, something he was convinced happened in a current-carrying wire. He was even more impressed by the fact that such patterns could be induced in one plate by bowing another nearby.

       

Such acoustic induction is apparently what lay behind his most famous experiment. On August 29, 1831, Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. What he expected was that a “wave” would be produced when the battery circuit was closed and that the wave would show up as a deflection of the galvanometer in the second circuit. He closed the primary circuit and, to his delight and satisfaction, saw the galvanometer needle jump.

       

A current had been induced in the secondary coil by one in the primary. When he opened the circuit, however, he was astonished to see the galvanometer jump in the opposite direction. Somehow, turning off the current also created an induced current in the secondary circuit, equal and opposite to the original current. This phenomenon led Faraday to propose what he called the “electrotonic” state of particles in the wire, which he considered a state of tension. A current thus appeared to be the setting up of such a state of tension or the collapse of such a state. Although he could not find experimental evidence for the electrotonic state, he never entirely abandoned the concept, and it shaped most of his later work.

       

In the fall of 1831 Faraday attempted to determine just how an induced current was produced. His original experiment had involved a powerful electromagnet, created by the winding of the primary coil. He now tried to create a current by using a permanent magnet. He discovered that when a permanent magnet was moved in and out of a coil of wire a current was induced in the coil. Magnets, he knew, were surrounded by forces that could be made visible by the simple expedient of sprinkling iron filings on a card held over them. Faraday saw the “lines of force” thus revealed as lines of tension in the medium, namely air, surrounding the magnet, and he soon discovered the law determining the production of electric currents by magnets: the magnitude of the current was dependent upon the number of lines of force cut by the conductor in unit time. He immediately realized that a continuous current could be produced by rotating a copper disk between the poles of a powerful magnet and taking leads off the disk’s rim and centre.

       

The outside of the disk would cut more lines than would the inside, and there would thus be a continuous current produced in the circuit linking the rim to the centre. This was the first dynamo. It was also the direct ancestor of electric motors, for it was only necessary to reverse the situation, to feed an electric current to the disk, to make it rotate.

       

On 29th August 1831, using his “induction ring", Faraday made one of his greatest discoveries - electromagnetic induction: the “induction” or generation of electricity in a wire by means of the electromagnetic effect of a current in another wire. The induction ring was the first electric transformer. In a second series of experiments in September he discovered magneto-electric induction: the production of a steady electric current. To do this, Faraday attached two wires through a sliding contact to a copper disc. By rotating the disc between the poles of a horseshoe magnet he obtained a continuous direct current. This was the first generator.

       

Although neither of Faraday’s devices is of practical use today they enhanced immeasurably the theoretical understanding of electricity and magnetism. He described these experiments in two papers presented to the Royal Society on 24th November 1831, and 12th January 1832. These were the first and second parts of his “Experimental researches into electricity” in which he gave his “law which governs the evolution of electricity by magneto-electric induction". After reading this, a young Frenchman, Hippolyte Pixii, constructed an electric generator that utilized the rotary motion between magnet and coil rather than Faraday’s to and fro motion in a straight line. All the generators in power stations today are direct descendants of the machine developed by Pixii from Faraday’s first principles.

       

It was characteristic of Faraday’s devotion to the enlargement of the bounds of human knowledge that on his discovery of magneto-electricity he abandoned the commercial work by which he had added to his small salary, in order to reserve all his energies for research. This financial loss was in part made up later by a pension of 300 pounds a year from the British Government.

       

Theory of electrochemistry:

       

While Faraday was performing these experiments and presenting them to the scientific world, doubts were raised about the identity of the different manifestations of electricity that had been studied. Were the electric “fluid” that apparently was released by electric eels and other electric fishes, that produced by a static electricity generator, that of the voltaic battery, and that of the new electromagnetic generator all the same? Or were they different fluids following different laws? Faraday was convinced that they were not fluids at all but forms of the same force, yet he recognized that this identity had never been satisfactorily shown by experiment. For this reason he began, in 1832, what promised to be a rather tedious attempt to prove that all electricities had precisely the same properties and caused precisely the same effects. The key effect was electrochemical decomposition.

       

Voltaic and electromagnetic electricity posed no problems, but static electricity did. As Faraday delved deeper into the problem, he made two startling discoveries. First, electrical force did not, as had long been supposed, act at a distance upon chemical molecules to cause them to dissociate. It was the passage of electricity through a conducting liquid medium that caused the molecules to dissociate, even when the electricity merely discharged into the air and did not pass into a “pole” or “centre of action” in a voltaic cell. Second, the amount of the decomposition was found to be related in a simple manner to the amount of electricity that passed through the solution.

       

These findings led Faraday to a new theory of electrochemistry. The electric force, he argued, threw the molecules of a solution into a state of tension (his electrotonic state). When the force was strong enough to distort the fields of forces that held the molecules together so as to permit the interaction of these fields with neighbouring particles, the tension was relieved by the migration of particles along the lines of tension, the different species of atoms migrating in opposite directions. The amount of electricity that passed, then, was clearly related to the chemical affinities of the substances in solution. These experiments led directly to Faraday’s two laws of electrochemistry: (1) The amount of a substance deposited on each electrode of an electrolytic cell is directly proportional to the quantity of electricity passed through the cell. (2) The quantities of different elements deposited by a given amount of electricity are in the ratio of their chemical equivalent weights.

       

Michael Faraday (1841/42)

       

Faraday’s work on electrochemistry provided him with an essential clue for the investigation of static electrical induction. Since the amount of electricity passed through the conducting medium of an electrolytic cell determined the amount of material deposited at the electrodes, why should not the amount of electricity induced in a nonconductor be dependent upon the material out of which it was made? In short, why should not every material have a specific inductive capacity? Every material does, and Faraday was the discoverer of this fact.

       

The portrate shown here was painted by Thomas Phillips (1770-1845), oil on canvas, The National Portrait Gallery, London.

       

Michael Faraday (ca. 1844-60)

       

By 1839 Faraday was able to bring forth a new and general theory of electrical action. Electricity, whatever it was, caused tensions to be created in matter. When these tensions were rapidly relieved (i.e., when bodies could not take much strain before “snapping” back), then what occurred was a rapid repetition of a cyclical buildup, breakdown, and buildup of tension that, like a wave, was passed along the substance.

       

Such substances were called conductors. In electrochemical processes the rate of buildup and breakdown of the strain was proportional to the chemical affinities of the substances involved, but again the current was not a material flow but a wave pattern of tensions and their relief. Insulators were simply materials whose particles could take an extraordinary amount of strain before they snapped. Electrostatic charge in an isolated insulator was simply a measure of this accumulated strain. Thus, all electrical action was the result of forced strains in bodies.

       

The strain on Faraday of eight years of sustained experimental and theoretical work was too much, and in 1839 his health broke down. For the next six years he did little creative science. Not until 1845 was he able to pick up the thread of his researches and extend his theoretical views.

       

Michael Faraday (ca. 1849) lithograph by W. Bosley from A. F. J. Claudet daguerreotype
Smithsonian Archives

       

Faraday had scientific discussions and collaborations with many famous scientists of his time.

       

Group of scientists: (from left to right) English physicist and chemist Michael Faraday (1791 - 1867), English biologist Thomas Huxley (1825 - 1895), English physicist Sir Charles Wheatley (1802 - 1875), Scottish physicist Sir David Brewster (1781 - 1868) and Irish physicist John Tyndall (1820 - 1893).

       

Later life:

       

Since the very beginning of his scientific work, Faraday had believed in what he called the unity of the forces of nature. By this he meant hat all the forces of nature were but manifestations of a single universal force and ought, therefore, to be convertible into one another. In 1846 he made public some of the speculations to which this view led him.

       

A lecturer, scheduled to deliver one of the Friday evening discourses at the Royal Institution by which Faraday encouraged the popularization of science, panicked at the last minute and ran out, leaving Faraday with a packed lecture hall and no lecturer. On the spur of the moment, Faraday offered “Thoughts on Ray Vibrations.” Specifically referring to point atoms and their infinite fields of force, he suggested that the lines of electric and magnetic force associated with these atoms might, in fact, serve as the medium by which light waves were propagated. Many years later, Maxwell was to build his electromagnetic field theory upon this speculation.

       

Professor Faraday delivering a lecture at the Royal Institution. Members of the Royal Instsitution attend a lecture given by Professor Faraday on Magnetism and Light, London 1846.

       

Inventor and scientist Michael Faraday lectures at the Royal Institution. The Prince Consort with his sons the Prince of Wales and the Duke of Edinburgh are seated in the front row facing Faraday. From a painting by Alexander Blaikley.

       

Every year on Christmas Day, he presented his Faraday Lectures for Children which were crowded with interested listeners. The Royal Institution Christmas lectures for children, begun by Faraday, continue to this day.

       

Faraday described his numerous experiments in electricity and electromagnetism in three volumes entitled Experimental Researches in Electricity (1839, 1844, 1855); his chemical work was chronicled in Experimental Researches in Chemistry and Physics (1858). Faraday ceased research work in 1855 because of declining mental powers, but he continued as a lecturer until 1861. A series of six children’s lectures published in 1860 as The Chemical History of a Candle, has become a classic of science literature.

       

When Faraday returned to active research in 1845, it was to tackle again a problem that had obsessed him for years, that of his hypothetical electrotonic state. He was still convinced that it must exist and that he simply had not yet discovered the means for detecting it. Once again he tried to find signs of intermolecular strain in substances through which electrical lines of force passed, but again with no success. It was at this time that a young Scot, William Thomson (later Lord Kelvin), wrote Faraday that he had studied Faraday’s papers on electricity and magnetism and that he, too, was convinced that some kind of strain must exist. He suggested that Faraday experiment with magnetic lines of force, since these could be produced at much greater strengths than could electrostatic ones.

       

Faraday took the suggestion, passed a beam of plane-polarized light through the optical glass of high refractive index that he had developed in the 1820s, and then turned on an electromagnet so that its lines of force ran parallel to the light ray. This time he was rewarded with success. The plane of polarization was rotated, indicating a strain in the molecules of the glass.

       

But Faraday again noted an unexpected result. When he changed the direction of the ray of light, the rotation remained in the same direction, a fact that Faraday correctly interpreted as meaning that the strain was not in the molecules of the glass but in the magnetic lines of force. The direction of rotation of the plane of polarization depended solely upon the polarity of the lines of force; the glass served merely to detect the effect. Faraday’s discovery (1845) that an intense magnetic field can rotate the plane of polarized light is known today as the Faraday effect. The phenomenon has been used to elucidate molecular structure and has yielded information about galactic magnetic fields.

       

This discovery confirmed Faraday’s faith in the unity of forces, and he plunged onward, certain that all matter must exhibit some response to a magnetic field. To his surprise he found that this was in fact so, but in a peculiar way. Some substances, such as iron, nickel, cobalt, and oxygen, lined up in a magnetic field so that the long axes of their crystalline or molecular structures were parallel to the lines of force; others lined up perpendicular to the lines of force.

       

Substances of the first class moved toward more intense magnetic fields; those of the second moved toward regions of less magnetic force. Faraday named the first group paramagnetics and the second diamagnetics. After further research he concluded that paramagnetics were bodies that conducted magnetic lines of force better than did the surrounding medium, whereas diamagnetics conducted them less well. By 1850 Faraday had evolved a radically new view of space and force. Space was not “nothing,” the mere location of bodies and forces, but a medium capable of supporting the strains of electric and magnetic forces. The energies of the world were not localized in the particles from which these forces arose but rather were to be found in the space surrounding them. Thus was born field theory. As Maxwell later freely admitted, the basic ideas for his mathematical theory of electrical and magnetic fields came from Faraday; his contribution was to mathematize those ideas in the form of his classical field equations.

       

Michael Faraday’s concern about contemporary environmental concerns caricatured. A cartoon depicting English chemist and physicist Professor Michael Faraday holding his nose from a smell as he gives his card to ‘Father Thames’.

       

From about 1855, Faraday’s mind began to fail. He still did occasional experiments, one of which involved attempting to find an electrical effect of raising a heavy weight, since he felt that gravity, like magnetism, must be convertible into some other force, most likely electrical. This time he was disappointed in his expectations, and the Royal Society refused to publish his negative results. More and more, Faraday began to sink into senility. Queen Victoria rewarded his lifetime of devotion to science by granting him the use of a house at Hampton Court and even offered him the honour of a knighthood. Faraday gratefully accepted the cottage but rejected the knighthood; he would, he said, remain plain Mr. Faraday to the end. In contrast to Davy, Faraday was known throughout his life as a kind and humble person, unconcerned with honors and eager to practice his science to the best of his ability. In 1865, Faraday ended his connection with the Royal Institution after over 50 years of service. He died at his house at Hampton Court on 25th August 1867 and was buried in Highgate Cemetery, London, leaving as his monument a new conception of physical reality.

       

His discoveries have had an incalculable effect on subsequent scientific and technical development. He was a true pioneer of scientific discovery. The discoveries made by Faraday were so numerous, and often demand so detailed a knowledge of chemistry and physics before they can be understood, that it is impossible to attempt to describe or even enumerate them here. Among the most important are the discovery of magneto-electric induction, of the law of electro-chemical decomposition, of the magnetization of light, and of diamagnetism.

       

Round each of these are grouped numbers of derivative but still highly important additions to scientific knowledge, and together they form so vast an achievement as to lead his successor, Tyndall, to say, “Taking him for all and all, I think it will be conceded that Michael Faraday was the greatest experimental philosopher the world has ever seen; and I will add the opinion, that the progress of future research will tend, not to dim or to diminish, but to enhance and glorify the labours of this mighty investigator.”

       

Two electrical units (for capacitance and charge) were named after Michael Faraday to honor his accomplishments:

       

Farad (F) is the SI unit of electric capacitance. Very early in the study of electricity scientists discovered that a pair of conductors separated by an insulator can store a much larger charge than an isolated conductor can store. The better the insulator, the larger the charge that the conductors can hold. This property of a circuit is called capacitance, and it is measured in farads.

       

One farad is defined as the ability to store one coulomb of charge per volt of potential difference between the two conductors. This is a natural definition, but the unit it defines is very large. In practical circuits, capacitance is often measured in microfarads, nanofarads, or sometimes even in picofarads (10-12 farad, or trillionths of a farad).

       

Faraday (Fd) is a unit of electric charge. In a process called electrolysis, chemists separate the components of a dissolved chemical compound by passing an electric current through the compound. The components are deposited at the electrodes, where the current enters or leaves the solution.

       

The British electrochemist and physicist Michael Faraday determined that the same amount of charge is needed to deposit one mole of any element or ion of valence one (meaning that each molecule of the ion has either one too many or one too few electrons). This amount of charge, equal to about 96.4853 kilocoulombs, became known as Faraday’s constant. Later, it was adopted as a convenient unit for measuring the charges used in electrolysis. One faraday is equal to the product of Avogadro’s number and the charge (1 e) on a single electron.


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