# Filip Ligmajer's Reviews > Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics

Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics

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page 61 | location 930-934 | Added on Thursday, 17 July 2014 16:21:50

By Ampère's theory, the magnetic force was simply what you got when you added all the straight-line forces between pairs of current elements mathematically. Faraday saw things differently—to him, the magnetic force that curved around any current-carrying wire was not an indirect, mathematically derived effect of straight-line forces, it was something primal, a circular force in its own right. The idea of a circular force was quite beyond the generally accepted doctrine of Newtonian forces, and Faraday's lack of a traditional scientific education probably made it easier for him to accept it.

page 63 | location 965-967 | Added on Thursday, 17 July 2014 16:26:05

In August 1831, Faraday wrote in his laboratory journal the first words for a new project that was to become his finest work. His Experimental Researches in Electricity, a monumental opus written entirely in words without a single formula, had begun.

page 65 | location 984-988 | Added on Thursday, 17 July 2014 16:29:33

Moreover, the patterns could be induced on the sand-strewn plate by stroking another plate a short distance away—vibrations in the first plate produced sound waves in the air that then caused the second plate to vibrate. As always, Faraday tried it for himself and explored every avenue by varying the conditions of the experiment. He was rewarded with an even more vivid demonstration of acoustic induction—when he poured a mixture of egg white, oil, and water on the second plate instead of sand, the vibrations showed up as very fine striations, a kind of crimping of the liquid mixture.

page 68 | location 1036-1042 | Added on Thursday, 17 July 2014 16:36:35

Faraday decided to try a variation on Arago's experiment. He mounted a copper disc on an axle and set its edge in a narrow gap between the poles of a powerful magnet. He then made an electrical circuit by placing one sliding contact on the edge of the disc, placing another on the axle, and connecting the two contacts by wires to a galvanometer. He hoped that when the disc rotated, its motion relative to the magnet would produce a steady current across the disc that would register on the galvanometer. He spun the disc and watched the needle. It moved, and this time stayed in its new position; there was a feeble but steady current. And when the disc was spun the other way, the needle also reversed its movement. Ten years after making the world's first electric motor, Faraday had made the world's first dynamo.

page 84 | location 1278-1282 | Added on Friday, 18 July 2014 08:40:09

In fact, these examples serve to remind us that he was working in completely unknown territory, struggling to make sense of the strange, and sometimes apparently contradictory, findings from his experiments. The wonder is not that he missed the odd point but that he somehow managed, from such confusing evidence, to produce ideas that were so unusual as to be almost impossible to describe in words, yet that turned out to be correct. Some of his ideas were not understood by anyone else until first the great physicist William Thomson (Lord Kelvin) and then James Clerk Maxwell, both Scotsmen from the following generation, expressed them in mathematical language.

page 89 | location 1360-1369 | Added on Friday, 18 July 2014 09:14:48

To Thomson, as to Ampère, mathematics was the language of science. Where Faraday had to do his own experiments to understand a topic, Thomson had to write his own equations. His first impression of Faraday's Experimental Researches in Electricity, which gave not a single equation, was that they seemed to be written in a perversely cumbersome foreign tongue, but once Thomson saw the analogy of lines of force with Fourier's mathematical theory of heat flow, he began to take the idea of lines of force seriously—the first person, apart from Faraday himself, to do so. He was intrigued to discover that exactly the same results could be derived from Coulomb's and Ampère's theory of electrostatic forces, so were Faraday's lines of force simply another way of formulating instantaneous action at a distance between point charges? Thomson thought so at first, but he noted Faraday's finding that electrical induction took time to act, rather like Fourier's heat flow; and he found that the using the analogy between lines of force and heat flow actually made some calculations a lot simpler. He began to think that Faraday could be right—that lines of force could have a physical existence and that electrical forces could be the manifestation of some kind of strain in the medium between the charged objects.

page 113 | location 1724-1732 | Added on Friday, 18 July 2014 10:49:51

It is difficult for us today to appreciate the immense importance then attached to saving lives (and cargoes) at sea. As late as 1912, the Nobel Prize in physics went to Niels Gustav Dalen for inventing a way of feeding gas automatically to lighthouses and buoys. His achievement, in the committee's judgment, had surpassed those of rival nominees Albert Einstein, Max Planck, Hendrik Antoon Lorentz, Ernst Mach, and Oliver Heaviside. Faraday's lighthouse work was a service to his fellow men, wholeheartedly given and well appreciated. And, rather appropriately, one of Faraday's comments on lighthouses illuminates for us how religious faith inspired his whole approach to scientific work. In a report, he wrote: There is no human arrangement that requires more regularity and certainty of operation than a lighthouse. It is trusted by the Mariner as if it were a law of nature, and as the Sun sets so he expects that, with the same certainty, the lights will appear.

page 116 | location 1773-1777 | Added on Friday, 18 July 2014 10:56:04

In 1897, the Dutch physicist Peter Zeeman repeated the experiment, using a stronger magnetic field and a more refined apparatus, and he found the very effect that Faraday had been looking for. The Zeeman effect, as it is known today—the splitting of the light spectrum into several components in the presence of a magnetic field—makes possible such techniques as magnetic resonance imaging. We can only wonder at the man who, even with fading mental powers, was able to envisage this effect of magnetism on light.

page 119 | location 1821-1830 | Added on Friday, 18 July 2014 11:02:20

Despite the universal acclamation of Faraday's scientific work, his greatest achievement had been largely ignored during his lifetime and was only beginning to surface at the time of his death. The great German physicist Hermann von Helmholtz made this tribute in 1881: Now that the mathematical interpretation of Faraday's conceptions regarding the nature of electric and magnetic forces has been given by Clerk Maxwell, we see how great a degree of exactness and precision was really hidden behind the words which to Faraday's contemporaries appeared either vague or obscure; and it is in the highest degree astonishing to see what a large number of general theorems, the methodical deduction of which requires the highest powers of mathematical analysis, he found by a kind of intuition, with the security of instinct, without the help of a single mathematical formula.15 A man of equal stature and complementary talents was needed to reveal Faraday's full greatness. That man was James Clerk Maxwell.

page 127 | location 1945-1951 | Added on Friday, 18 July 2014 13:21:50

John Clerk Maxwell's plan was for his son to become a lawyer—a more successful one than he himself had been. This seems odd, given his son's obvious gift for science and his own fascination for technology, but his judgment was not wholly at fault this time. Science, then called natural philosophy, was generally thought to be an excellent hobby for a gentleman but a poor career choice: It was poorly paid and opportunities were sparse because there were few professional posts and the post-holders tended to remain for life, as Faraday did at the Royal Institution. Strange as it seems to us, science was not even thought to be particularly useful, as most of the great advances in industry and transport had been introduced and developed not by natural philosophers but by practical men with little theoretical knowledge, like Abraham Darby, the inventor of coke smelting, and George Stephenson, known as “the Father of railways.”

page 149 | location 2280-2284 | Added on Saturday, 19 July 2014 09:58:44

Scanning the books and papers that Thomson had recommended, Maxwell soon saw that the state of knowledge about electricity and magnetism was unsatisfactory. Much had been written, but each leading author had his own methods, terminology, and point of view. All the theories except Faraday's were mathematical and based on the idea of action at a distance. Their authors had largely spurned Faraday's notion of lines of force because it couldn't be expressed in mathematical terms, except, in a limited way, through an analogy Thomson had made between electric lines of force and the steady flow of heat through a metal bar.

page 152 | location 2325-2330 | Added on Saturday, 19 July 2014 10:07:51

and to each point on each sink. Electric and magnetic forces were known to follow a similar law—the force between two electric charges or two magnetic poles was inversely proportional to the square of their distance apart—so the basis of the analogy was set. The direction and speed of flow of fluid at any point represented the direction and strength of either the electric force or the magnetic force; the faster the flow, the stronger the force. It was a strange analogy—moving fluid representing static force—but it served Maxwell's purpose. And the beauty of it all was that the streamlines of fluid flow represented Faraday's electric or magnetic lines of force.

page 171 | location 2607-2619 | Added on Saturday, 19 July 2014 11:24:24

Maxwell wrote up his new law and in the same paper made the important and surprising prediction that the viscosity of a gas, its internal friction, was independent of pressure. This happened because, at higher pressure, the dragging effect on a moving body of being surrounded by more molecules was exactly counteracted by the screening effect they provided. It was vital for the prediction to be tested by experiment—a verdict of false would demolish the whole kinetic theory, but a verdict of true would greatly strengthen it. As we will see, Maxwell later managed to do the experiment at home, with much help from Katherine. Elsewhere in the paper Maxwell made mistakes; he was off by a factor of 8,000 in one calculation because he had forgotten to convert kilograms to pounds and hours to seconds! Despite the flaws, his paper “Illustrations of the Dynamical Theory of Gases” drew gasps of admiration and put Maxwell in the first rank of physicists. However, the first person to recognize Maxwell's full achievement in bringing statistics into physics was at that time a schoolboy in Vienna, and he didn't see the paper until five years later. Ludwig Boltzmann was then so inspired by Maxwell's work on kinetic theory that he spent most of his career developing the subject further. The two began a kind of tennis match that lasted all of Maxwell's life; each in turn would be inspired by the other's work and counter with a further extension of the theory. Though they never thought of themselves as such, they were, in effect, a magnificent partnership, and it is pleasing that their names are linked in the Maxwell-Boltzmann distribution of molecular energies.

page 171 | location 2619-2622 | Added on Saturday, 19 July 2014 11:25:46

For all his strong and progressive ideas on teaching, he was, sadly, not very good at it himself. Yet the students liked him. They were allowed to borrow only two books at a time from the college library, but Maxwell took out more for them, something professors were allowed to do for friends, and, when challenged, he replied that the students were his friends.

page 190 | location 2908-2915 | Added on Saturday, 19 July 2014 18:27:31

He had united electricity, magnetism, and light—a stupendous achievement. Yet his announcement caused barely a ripple. As physicists generally believed that an aether of some kind was necessary for the propagation of light, one might have expected them to accept Maxwell's extension of the principle to electricity and magnetism. But his model seemed so weird and cumbersome that nobody thought it could possibly represent reality. The reaction of his friend Cecil Monro was typical: The coincidence between the observed velocity of light and your calculated velocity of a transverse vibration in your medium seems a brilliant result. But I must say I think a few such results are needed before you can get people to think that every time an electric current is produced a little file of particles is squeezed along between two rows of wheels.

page 191 | location 2918-2921 | Added on Saturday, 19 July 2014 18:28:33

Despite all his warnings, people couldn't understand that Maxwell's model didn't purport to represent nature's actual mechanism, but that it was merely a temporary aid to thought, a means of arriving at the relevant mathematical relationships by using an analogy. His analogy happened to use spinning cells, but that was by the way; it was the mathematical relationships that were important.

page 191 | location 2928-2934 | Added on Saturday, 19 July 2014 18:30:26

According to Newton, the gravitational force between two masses was proportional to their product divided by the square of the distance between them. Simply replace masses with charges or pole strengths, and you had the basic laws of electricity and magnetism. But with the work of Coulomb, Ampère, Poisson, and others had come an assumption that the forces resulted from instantaneous action at a distance between the masses, poles, or charges. Newton himself had been careful not to make any such assumption—indeed, he had, as we've seen, described action at a distance as “so great an absurdity, that I believe no man, who has in philosophical matters a competent way of thinking, can ever fall into it.”12 But this warning had been forgotten, and throughout the early and middle 1800s, the only prominent physicists to challenge action at a distance openly were Faraday and Maxwell.

page 196 | location 3004-3010 | Added on Saturday, 19 July 2014 21:50:38

In his first paper on electricity and magnetism, he had used the analogy of an incompressible fluid to give mathematical expression to Faraday's concept of lines of force. In his second, he had built an entirely different imaginary model from spinning cells and idle wheels—a model that he admitted was “somewhat cumbersome”—but one that had yielded remarkable results. With it, he had not only accounted for all known electromagnetic effects but also had predicted two startling new ones: (1) displacement currents and (2) electromagnetic waves that traveled at the speed of light. Even the most enlightened of his contemporaries thought that the next step would be to refine this rather bizarre model, but, instead, Maxwell decided to put the model to one side and build the theory ab initio using only the principles of dynamics.

page 196 | location 3003-3010 | Added on Saturday, 19 July 2014 21:50:56

Maxwell was unique in the way he could return to a topic and raise it to new heights by taking a completely fresh approach. In his first paper on electricity and magnetism, he had used the analogy of an incompressible fluid to give mathematical expression to Faraday's concept of lines of force. In his second, he had built an entirely different imaginary model from spinning cells and idle wheels—a model that he admitted was “somewhat cumbersome”—but one that had yielded remarkable results. With it, he had not only accounted for all known electromagnetic effects but also had predicted two startling new ones: (1) displacement currents and (2) electromagnetic waves that traveled at the speed of light. Even the most enlightened of his contemporaries thought that the next step would be to refine this rather bizarre model, but, instead, Maxwell decided to put the model to one side and build the theory ab initio using only the principles of dynamics.

page 213 | location 3264-3265 | Added on Saturday, 19 July 2014 22:30:13

Oddly, it was Maxwell's less frolicsome colleague William Thomson who named the demon; Maxwell wanted to call him a valve!

page 214 | location 3276-3283 | Added on Saturday, 19 July 2014 22:34:02

Curl is the essence of the relationship between electricity and magnetism; it explains how the force of each connects with the flux of the other. At any given point in space, any vector, like magnetic flux or the velocity of wind in air, has a curl, which is itself a vector, though it may take the value of zero. Curl isn't easy to visualize, but it can be done. Think of water flowing in a river. The vector here is the speed and direction of flow, and, in general, it varies from point to point in the river. Now imagine a tiny paddle wheel somehow fixed at a point in the river but with its axis free to take up any angle. If (and only if) the water is flowing faster on one side of the paddle wheel than the other, the wheel will spin, and its axis will take up the position that makes it spin fastest. The curl of the water flow at out point is a vector whose magnitude is proportional to the rate of spin and whose direction is along the axis of spin, by convention in the direction a right-handed screw would move if it turned the same way as the paddle wheel.

page 217 | location 3319-3323 | Added on Saturday, 19 July 2014 22:39:22

Only the final equations appeared in the alternative quaternion format, as a kind of optional extra—one that most people preferred to do without. So things were to stay until six years after Maxwell's death, when Oliver Heaviside reduced the number of equations to four and replaced the quaternion representation with a much simpler kind of vector algebra. He thereby incurred the fury of Tait, who accused him of mutilating Hamilton's beautiful quaternions, but, as we'll see in a later chapter, Heaviside gave as good as he got—both of them were masters of literary invective and enjoyed a good scrap.

page 225 | location 3450-3456 | Added on Sunday, 20 July 2014 08:12:04

Henry Cavendish had also been ahead of his time. When Maxwell looked through Cavendish's accounts of electrical experiments performed a hundred years earlier, he was astonished. It was like finding a dozen unpublished plays by Shakespeare. Among a string of stupendous results, Cavendish had demonstrated the inverse-square law for the force between electrical charges more effectively than Coulomb, after whom the law was named. He had also discovered Ohm's law fifty years before Ohm and twenty years before Volta produced the first electric battery. His method was simple and painful. He connected two wires to the oppositely charged parts of a Leyden jar and grasped both wires in one hand. He then repeated the procedure with various circuit arrangements, each time judging the strength of the current by measuring how far up his arm he could feel the shock.

by

page 61 | location 930-934 | Added on Thursday, 17 July 2014 16:21:50

By Ampère's theory, the magnetic force was simply what you got when you added all the straight-line forces between pairs of current elements mathematically. Faraday saw things differently—to him, the magnetic force that curved around any current-carrying wire was not an indirect, mathematically derived effect of straight-line forces, it was something primal, a circular force in its own right. The idea of a circular force was quite beyond the generally accepted doctrine of Newtonian forces, and Faraday's lack of a traditional scientific education probably made it easier for him to accept it.

page 63 | location 965-967 | Added on Thursday, 17 July 2014 16:26:05

In August 1831, Faraday wrote in his laboratory journal the first words for a new project that was to become his finest work. His Experimental Researches in Electricity, a monumental opus written entirely in words without a single formula, had begun.

page 65 | location 984-988 | Added on Thursday, 17 July 2014 16:29:33

Moreover, the patterns could be induced on the sand-strewn plate by stroking another plate a short distance away—vibrations in the first plate produced sound waves in the air that then caused the second plate to vibrate. As always, Faraday tried it for himself and explored every avenue by varying the conditions of the experiment. He was rewarded with an even more vivid demonstration of acoustic induction—when he poured a mixture of egg white, oil, and water on the second plate instead of sand, the vibrations showed up as very fine striations, a kind of crimping of the liquid mixture.

page 68 | location 1036-1042 | Added on Thursday, 17 July 2014 16:36:35

Faraday decided to try a variation on Arago's experiment. He mounted a copper disc on an axle and set its edge in a narrow gap between the poles of a powerful magnet. He then made an electrical circuit by placing one sliding contact on the edge of the disc, placing another on the axle, and connecting the two contacts by wires to a galvanometer. He hoped that when the disc rotated, its motion relative to the magnet would produce a steady current across the disc that would register on the galvanometer. He spun the disc and watched the needle. It moved, and this time stayed in its new position; there was a feeble but steady current. And when the disc was spun the other way, the needle also reversed its movement. Ten years after making the world's first electric motor, Faraday had made the world's first dynamo.

page 84 | location 1278-1282 | Added on Friday, 18 July 2014 08:40:09

In fact, these examples serve to remind us that he was working in completely unknown territory, struggling to make sense of the strange, and sometimes apparently contradictory, findings from his experiments. The wonder is not that he missed the odd point but that he somehow managed, from such confusing evidence, to produce ideas that were so unusual as to be almost impossible to describe in words, yet that turned out to be correct. Some of his ideas were not understood by anyone else until first the great physicist William Thomson (Lord Kelvin) and then James Clerk Maxwell, both Scotsmen from the following generation, expressed them in mathematical language.

page 89 | location 1360-1369 | Added on Friday, 18 July 2014 09:14:48

To Thomson, as to Ampère, mathematics was the language of science. Where Faraday had to do his own experiments to understand a topic, Thomson had to write his own equations. His first impression of Faraday's Experimental Researches in Electricity, which gave not a single equation, was that they seemed to be written in a perversely cumbersome foreign tongue, but once Thomson saw the analogy of lines of force with Fourier's mathematical theory of heat flow, he began to take the idea of lines of force seriously—the first person, apart from Faraday himself, to do so. He was intrigued to discover that exactly the same results could be derived from Coulomb's and Ampère's theory of electrostatic forces, so were Faraday's lines of force simply another way of formulating instantaneous action at a distance between point charges? Thomson thought so at first, but he noted Faraday's finding that electrical induction took time to act, rather like Fourier's heat flow; and he found that the using the analogy between lines of force and heat flow actually made some calculations a lot simpler. He began to think that Faraday could be right—that lines of force could have a physical existence and that electrical forces could be the manifestation of some kind of strain in the medium between the charged objects.

page 113 | location 1724-1732 | Added on Friday, 18 July 2014 10:49:51

It is difficult for us today to appreciate the immense importance then attached to saving lives (and cargoes) at sea. As late as 1912, the Nobel Prize in physics went to Niels Gustav Dalen for inventing a way of feeding gas automatically to lighthouses and buoys. His achievement, in the committee's judgment, had surpassed those of rival nominees Albert Einstein, Max Planck, Hendrik Antoon Lorentz, Ernst Mach, and Oliver Heaviside. Faraday's lighthouse work was a service to his fellow men, wholeheartedly given and well appreciated. And, rather appropriately, one of Faraday's comments on lighthouses illuminates for us how religious faith inspired his whole approach to scientific work. In a report, he wrote: There is no human arrangement that requires more regularity and certainty of operation than a lighthouse. It is trusted by the Mariner as if it were a law of nature, and as the Sun sets so he expects that, with the same certainty, the lights will appear.

page 116 | location 1773-1777 | Added on Friday, 18 July 2014 10:56:04

In 1897, the Dutch physicist Peter Zeeman repeated the experiment, using a stronger magnetic field and a more refined apparatus, and he found the very effect that Faraday had been looking for. The Zeeman effect, as it is known today—the splitting of the light spectrum into several components in the presence of a magnetic field—makes possible such techniques as magnetic resonance imaging. We can only wonder at the man who, even with fading mental powers, was able to envisage this effect of magnetism on light.

page 119 | location 1821-1830 | Added on Friday, 18 July 2014 11:02:20

Despite the universal acclamation of Faraday's scientific work, his greatest achievement had been largely ignored during his lifetime and was only beginning to surface at the time of his death. The great German physicist Hermann von Helmholtz made this tribute in 1881: Now that the mathematical interpretation of Faraday's conceptions regarding the nature of electric and magnetic forces has been given by Clerk Maxwell, we see how great a degree of exactness and precision was really hidden behind the words which to Faraday's contemporaries appeared either vague or obscure; and it is in the highest degree astonishing to see what a large number of general theorems, the methodical deduction of which requires the highest powers of mathematical analysis, he found by a kind of intuition, with the security of instinct, without the help of a single mathematical formula.15 A man of equal stature and complementary talents was needed to reveal Faraday's full greatness. That man was James Clerk Maxwell.

page 127 | location 1945-1951 | Added on Friday, 18 July 2014 13:21:50

John Clerk Maxwell's plan was for his son to become a lawyer—a more successful one than he himself had been. This seems odd, given his son's obvious gift for science and his own fascination for technology, but his judgment was not wholly at fault this time. Science, then called natural philosophy, was generally thought to be an excellent hobby for a gentleman but a poor career choice: It was poorly paid and opportunities were sparse because there were few professional posts and the post-holders tended to remain for life, as Faraday did at the Royal Institution. Strange as it seems to us, science was not even thought to be particularly useful, as most of the great advances in industry and transport had been introduced and developed not by natural philosophers but by practical men with little theoretical knowledge, like Abraham Darby, the inventor of coke smelting, and George Stephenson, known as “the Father of railways.”

page 149 | location 2280-2284 | Added on Saturday, 19 July 2014 09:58:44

Scanning the books and papers that Thomson had recommended, Maxwell soon saw that the state of knowledge about electricity and magnetism was unsatisfactory. Much had been written, but each leading author had his own methods, terminology, and point of view. All the theories except Faraday's were mathematical and based on the idea of action at a distance. Their authors had largely spurned Faraday's notion of lines of force because it couldn't be expressed in mathematical terms, except, in a limited way, through an analogy Thomson had made between electric lines of force and the steady flow of heat through a metal bar.

page 152 | location 2325-2330 | Added on Saturday, 19 July 2014 10:07:51

and to each point on each sink. Electric and magnetic forces were known to follow a similar law—the force between two electric charges or two magnetic poles was inversely proportional to the square of their distance apart—so the basis of the analogy was set. The direction and speed of flow of fluid at any point represented the direction and strength of either the electric force or the magnetic force; the faster the flow, the stronger the force. It was a strange analogy—moving fluid representing static force—but it served Maxwell's purpose. And the beauty of it all was that the streamlines of fluid flow represented Faraday's electric or magnetic lines of force.

page 171 | location 2607-2619 | Added on Saturday, 19 July 2014 11:24:24

Maxwell wrote up his new law and in the same paper made the important and surprising prediction that the viscosity of a gas, its internal friction, was independent of pressure. This happened because, at higher pressure, the dragging effect on a moving body of being surrounded by more molecules was exactly counteracted by the screening effect they provided. It was vital for the prediction to be tested by experiment—a verdict of false would demolish the whole kinetic theory, but a verdict of true would greatly strengthen it. As we will see, Maxwell later managed to do the experiment at home, with much help from Katherine. Elsewhere in the paper Maxwell made mistakes; he was off by a factor of 8,000 in one calculation because he had forgotten to convert kilograms to pounds and hours to seconds! Despite the flaws, his paper “Illustrations of the Dynamical Theory of Gases” drew gasps of admiration and put Maxwell in the first rank of physicists. However, the first person to recognize Maxwell's full achievement in bringing statistics into physics was at that time a schoolboy in Vienna, and he didn't see the paper until five years later. Ludwig Boltzmann was then so inspired by Maxwell's work on kinetic theory that he spent most of his career developing the subject further. The two began a kind of tennis match that lasted all of Maxwell's life; each in turn would be inspired by the other's work and counter with a further extension of the theory. Though they never thought of themselves as such, they were, in effect, a magnificent partnership, and it is pleasing that their names are linked in the Maxwell-Boltzmann distribution of molecular energies.

page 171 | location 2619-2622 | Added on Saturday, 19 July 2014 11:25:46

For all his strong and progressive ideas on teaching, he was, sadly, not very good at it himself. Yet the students liked him. They were allowed to borrow only two books at a time from the college library, but Maxwell took out more for them, something professors were allowed to do for friends, and, when challenged, he replied that the students were his friends.

page 190 | location 2908-2915 | Added on Saturday, 19 July 2014 18:27:31

He had united electricity, magnetism, and light—a stupendous achievement. Yet his announcement caused barely a ripple. As physicists generally believed that an aether of some kind was necessary for the propagation of light, one might have expected them to accept Maxwell's extension of the principle to electricity and magnetism. But his model seemed so weird and cumbersome that nobody thought it could possibly represent reality. The reaction of his friend Cecil Monro was typical: The coincidence between the observed velocity of light and your calculated velocity of a transverse vibration in your medium seems a brilliant result. But I must say I think a few such results are needed before you can get people to think that every time an electric current is produced a little file of particles is squeezed along between two rows of wheels.

page 191 | location 2918-2921 | Added on Saturday, 19 July 2014 18:28:33

Despite all his warnings, people couldn't understand that Maxwell's model didn't purport to represent nature's actual mechanism, but that it was merely a temporary aid to thought, a means of arriving at the relevant mathematical relationships by using an analogy. His analogy happened to use spinning cells, but that was by the way; it was the mathematical relationships that were important.

page 191 | location 2928-2934 | Added on Saturday, 19 July 2014 18:30:26

According to Newton, the gravitational force between two masses was proportional to their product divided by the square of the distance between them. Simply replace masses with charges or pole strengths, and you had the basic laws of electricity and magnetism. But with the work of Coulomb, Ampère, Poisson, and others had come an assumption that the forces resulted from instantaneous action at a distance between the masses, poles, or charges. Newton himself had been careful not to make any such assumption—indeed, he had, as we've seen, described action at a distance as “so great an absurdity, that I believe no man, who has in philosophical matters a competent way of thinking, can ever fall into it.”12 But this warning had been forgotten, and throughout the early and middle 1800s, the only prominent physicists to challenge action at a distance openly were Faraday and Maxwell.

page 196 | location 3004-3010 | Added on Saturday, 19 July 2014 21:50:38

In his first paper on electricity and magnetism, he had used the analogy of an incompressible fluid to give mathematical expression to Faraday's concept of lines of force. In his second, he had built an entirely different imaginary model from spinning cells and idle wheels—a model that he admitted was “somewhat cumbersome”—but one that had yielded remarkable results. With it, he had not only accounted for all known electromagnetic effects but also had predicted two startling new ones: (1) displacement currents and (2) electromagnetic waves that traveled at the speed of light. Even the most enlightened of his contemporaries thought that the next step would be to refine this rather bizarre model, but, instead, Maxwell decided to put the model to one side and build the theory ab initio using only the principles of dynamics.

page 196 | location 3003-3010 | Added on Saturday, 19 July 2014 21:50:56

Maxwell was unique in the way he could return to a topic and raise it to new heights by taking a completely fresh approach. In his first paper on electricity and magnetism, he had used the analogy of an incompressible fluid to give mathematical expression to Faraday's concept of lines of force. In his second, he had built an entirely different imaginary model from spinning cells and idle wheels—a model that he admitted was “somewhat cumbersome”—but one that had yielded remarkable results. With it, he had not only accounted for all known electromagnetic effects but also had predicted two startling new ones: (1) displacement currents and (2) electromagnetic waves that traveled at the speed of light. Even the most enlightened of his contemporaries thought that the next step would be to refine this rather bizarre model, but, instead, Maxwell decided to put the model to one side and build the theory ab initio using only the principles of dynamics.

page 213 | location 3264-3265 | Added on Saturday, 19 July 2014 22:30:13

Oddly, it was Maxwell's less frolicsome colleague William Thomson who named the demon; Maxwell wanted to call him a valve!

page 214 | location 3276-3283 | Added on Saturday, 19 July 2014 22:34:02

Curl is the essence of the relationship between electricity and magnetism; it explains how the force of each connects with the flux of the other. At any given point in space, any vector, like magnetic flux or the velocity of wind in air, has a curl, which is itself a vector, though it may take the value of zero. Curl isn't easy to visualize, but it can be done. Think of water flowing in a river. The vector here is the speed and direction of flow, and, in general, it varies from point to point in the river. Now imagine a tiny paddle wheel somehow fixed at a point in the river but with its axis free to take up any angle. If (and only if) the water is flowing faster on one side of the paddle wheel than the other, the wheel will spin, and its axis will take up the position that makes it spin fastest. The curl of the water flow at out point is a vector whose magnitude is proportional to the rate of spin and whose direction is along the axis of spin, by convention in the direction a right-handed screw would move if it turned the same way as the paddle wheel.

page 217 | location 3319-3323 | Added on Saturday, 19 July 2014 22:39:22

Only the final equations appeared in the alternative quaternion format, as a kind of optional extra—one that most people preferred to do without. So things were to stay until six years after Maxwell's death, when Oliver Heaviside reduced the number of equations to four and replaced the quaternion representation with a much simpler kind of vector algebra. He thereby incurred the fury of Tait, who accused him of mutilating Hamilton's beautiful quaternions, but, as we'll see in a later chapter, Heaviside gave as good as he got—both of them were masters of literary invective and enjoyed a good scrap.

page 225 | location 3450-3456 | Added on Sunday, 20 July 2014 08:12:04

Henry Cavendish had also been ahead of his time. When Maxwell looked through Cavendish's accounts of electrical experiments performed a hundred years earlier, he was astonished. It was like finding a dozen unpublished plays by Shakespeare. Among a string of stupendous results, Cavendish had demonstrated the inverse-square law for the force between electrical charges more effectively than Coulomb, after whom the law was named. He had also discovered Ohm's law fifty years before Ohm and twenty years before Volta produced the first electric battery. His method was simple and painful. He connected two wires to the oppositely charged parts of a Leyden jar and grasped both wires in one hand. He then repeated the procedure with various circuit arrangements, each time judging the strength of the current by measuring how far up his arm he could feel the shock.

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*Faraday, Maxwell, and the Electromagnetic Field*.## Reading Progress

Finished Reading

August 27, 2014
– Shelved