The Physics Book

When there is a large store of When a system has low ENERGY AND MATTER 99 internal heat energy, internal heat energy, temperature is high. Time’s arrow temperature is low. The significance of the Heat flows from hot areas to cold areas. discovery of the second law of thermodynamics is often Heat naturally dissipates (spreads out) over time. overlooked, because other scientists quickly built on The degree of dissipation, or entropy, of the the work of Clausius and universe tends to a maximum. his peers. In fact, the second law of thermodynamics is called it “equivalence value,” with Thomson came up with a way as crucial to physics as of describing the second law of Newton’s discovery of the one equation for S (entropy) for thermodynamics in relation to the laws of motion, and it played limits of heat engines. This became a key part in modifying the open energy systems and another the basis of what is now known Newtonian vision of the for closed systems. An energy as the Kelvin-Planck statement of universe that had prevailed system is a region where energy the law (Lord Kelvin was the title until then. flows—it could be a car engine or Thomson took when given a the entire atmosphere. An open peerage in 1892). German physicist In Newton’s universe, all system can exchange both energy Max Planck refined Kelvin’s idea actions happen equally in and matter with its surroundings; so that it read: “it is impossible to every direction, so time has a closed system can only exchange devise a cyclically operating heat no direction—like an eternal energy (as heat or work). engine, the effect of which is to mechanism that can be run absorb energy in the form of heat backward or forward. Within a finite period of time from a single thermal reservoir and Clausius’s second law of to come the earth again must to deliver an equivalent amount thermodynamics overturned be unfit for human habitation. of work.” In other words, it is this view. If heat flows one impossible to make a heat engine way, so must time. Things William Thomson that is 100 percent efficient. It is decay, run down, come to an not easy to see that this is what end, and time’s arrow points Clausius was also saying, which in one direction only—toward has caused confusion ever since. the end. The implications of Essentially, these ideas are all based this discovery shook many on the same thermodynamics law: people of religious faith who the inevitability of heat loss when believed that the universe heat flows one way. ■ was everlasting. Once a candle has been burned, the wax that was burned cannot be restored. The thermodynamic arrow of time points in one direction: toward the end.

100 IN CONTEXT IBTTHESCEVOFAMLPUEOIORDNAEND KEY FIGURE Johannes Diderik CHANGES OF STATE AND MAKING BONDS van der Waals (1837–1923) BEFORE c. 75 bce The Roman thinker Lucretius suggests liquids are made from smooth round atoms but solids are bound together by hooked atoms. 1704 Isaac Newton theorizes that atoms are held together by an invisible force of attraction. 1869 Irish chemist and physicist Thomas Andrews discovers the continuity between the two fluid states of matter—liquid and gas. AFTER 1898 Scottish chemist James Dewar liquefies hydrogen. 1908 Dutch physicist Heike Kamerlingh Onnes liquefies helium. I t has long been known that the same substance can exist in at least three phases—solid, liquid, and gas. Water, for example, can be ice, liquid water, and vapor. But what was going on in the changes between these phases seemed for much of the 19th century to present an obstacle to the gas laws that had been established in the late 18th century. A particular focus was the two fluid states—liquid and gas. In both states, the substance flows to take up the shape of any container, and it cannot hold its own shape like a solid. Scientists had shown that if a gas is compressed more and more, its pressure does not

ENERGY AND MATTER 101 See also: Models of matter 68–71 ■ Fluids 76–79 ■ Heat and transfers 80–81 ■ The gas laws 82–85 ■ Entropy and the second law of thermodynamics 94–99 ■ The development of statistical mechanics 104–111 How am I to name this point (362°C), at which point no splashing temperature, pressure, and volume, at which the fluid and its was heard. The boundary between and how it might affect the phases the gas and the liquid was gone. of a substance. In 1869, he described vapor become one according experiments in which he trapped to a law of continuity? It was known that keeping a carbon dioxide above mercury in a Michael Faraday liquid under pressure can stop it glass tube. By pushing the mercury all turning to gas, but de la Tour’s up, he could raise the pressure of In a letter to fellow scientist, experiments revealed that there is the gas until it turned liquid. Yet it William Whewell (1844) a temperature at which a liquid will would never liquefy above 91.26°F always turn to gas, no matter how (32.92°C), no matter how much increase indefinitely, and eventually much pressure it is subjected to. pressure he applied. He called this it turns to liquid. Similarly, if a At this temperature, there is no temperature the “critical point” of liquid is heated, a little evaporates distinction between the liquid carbon dioxide. Andrews further at first, and then eventually all of it phase and the gas phase—both observed, “We have seen that the evaporates. The boiling point of become equally dense. Decreasing gaseous and liquid phases are water—the maximum temperature the temperature then restores the essentially only distinct stages of that water can reach—is easily differences between the phases. one and the same state of matter measured, and this measurably and that they are able to go into each rises under pressure, which is the The point where liquid and other by a continuous change.” principle behind a pressure cooker. gas are in equilibrium remained a vague concept until the 1860s, The idea of the continuity The points of change when physicist Thomas Andrews between the liquid and gas phases Scientists wanted to go beyond investigated the phenomenon. He was a key insight, highlighting ❯❯ these observations to know what studied the relationship between happens within a substance when liquid changes to gas. In 1822, PRESSURE (ATMOSPHERE, OR ATM) 218 Water Critical point French engineer and physicist Normal Normal Baron Charles Cagniard de la Tour freezing Steam boiling point experimented with a “steam point Water vapor digester,” a pressurized device that generated steam from water heated 1 Ice beyond its normal boiling point. He 0.006 partially filled the digester cylinder with water and dropped a flint ball Triple point 32 212 705 into it. Rolling the cylinder like a log, TEMPERATURE (ºF) he could hear the ball splashing as it met the water. The cylinder A phase diagram plots the temperature and pressure at which a was then heated to a temperature, substance—in this case, water—is solid, liquid, or gas. At the “triple estimated by de la Tour to be 683.6°F point,” a substance can exist simultaneously as a solid, a liquid, and a gas. At the critical point, a liquid and its gas become identical.

102 CHANGES OF STATE AND MAKING BONDS In a liquid, molecules Heat gives molecules forces occur in “polar” molecules, move but are bound the energy to move where electrons are shared unequally between the atoms of weakly together. more quickly. the molecule. In hydrochloric acid, for example, the chlorine atom The liquid turns to a gas Some move so quickly that has an extra electron, taken from when most molecules they break away from the the hydrogen atom. This gives the move too quickly to chlorine part of the molecule a stick together. surface of the liquid. slight negative charge, unlike the hydrogen part. The result is that their fundamental similarity. developed a key “equation of state” in liquid hydrochloric acid solution, What had yet to be discovered, to mathematically describe the negative sides of some molecules though, were the forces that lay behavior of gases and their are attracted to the positive sides of behind these different phases of condensation to liquid, which could others—this binds them together. matter and how they interacted. be applied to different substances. London dispersion force (named Molecular ties Van der Waals’ work helped after German–American scientist Early in the 19th century, British establish the reality of molecules Fritz London, who first recognized scientist Thomas Young suggested and identify intermolecular bonds. it in 1930) occurs between nonpolar that the surface of a liquid is held These are far weaker than the molecules. For example, in chlorine together by intermolecular bonds. bonds between atoms, which are gas the two atoms in each molecule It is this “surface tension” that pulls based on powerful electrostatic are equally charged on either side. water into drops and forms a curve forces. Molecules of the same But, the electrons in an atom are on the top of a glass of water, as substance are held together constantly moving. This means the molecules are drawn together. differently, in both the liquid and that one side of the molecule may This work was taken further by the gas phases. For instance, the bonds become briefly negative while the Dutch physicist Johannes Diderik that bind water molecules are not other becomes briefly positive, van der Waals, who looked at what the same as the bonds that tie so bonds within molecules are happened when the surface tension together oxygen and hydrogen constantly formed and reformed. broke and allowed the molecules to atoms within each water molecule. break away, turning liquid water The third force, the hydrogen into water vapor. When a liquid is turned to a gas, bond, is a special kind of dipole– the forces between the molecules dipole bond that occurs within Van der Waals proposed that need to be overcome to allow those hydrogen. It is the interaction the change in state is part of a molecules to move freely. Heat between a hydrogen atom and an continuum and not a distinct break provides the energy to make the atom of either oxygen, fluorine, or between liquid and gas. There molecules vibrate. Once the nitrogen. It is especially strong for is a transition layer in which vibrations are powerful enough, the an intermolecular bond because the water is neither exclusively molecules break free of the forces liquid nor gas. He found that as that bind them and become gas. I was quite convinced of the temperature rises, surface tension real existence of molecules. diminishes, and at the critical Forces of attraction temperature surface tension Three key forces of intermolecular Johannes Diderik vanishes altogether, allowing the attraction—dipole–dipole, London van der Waals transition layer to become infinitely dispersion, and hydrogen bond— thick. Van der Waals then gradually have become known collectively as Van der Waals forces. Dipole–dipole

oxygen, fluorine, and nitrogen There can be no doubt that ENERGY AND MATTER 103 atoms are strong attractors of the name of van der Waals electrons, while hydrogen is prone Johannes Diderik van to losing them. So, a molecule that will soon be among the der Waals combines them becomes strongly foremost in molecular science. polar, creating, for instance, the Born the son of a carpenter robust hydrogen bonds that hold James Clerk Maxwell in the Dutch city of Leiden in water (H2O) together. 1837, Johannes Diderik van and back again. His “equation of der Waals lacked sufficient Dispersion bonds are the state” enabled critical points to be schooling to enter higher weakest of the van der Waals found for a range of substances, education. He became a forces. Some elements that are making it possible to liquefy gases teacher of mathematics and bound together by them, such as such as oxygen, nitrogen, and physics and studied part-time chlorine and fluorine, remain as a helium. It also led to the discovery of at Leiden University, finally gas unless cooled to an extremely superconductors—substances that achieving his doctorate—in low temperature (-306.4°F [-188°C] lose all electrical resistance when molecular attraction—in 1873. and -302.8°F [-186°C] respectively), cooled to ultra-low temperatures. ■ when the bonds become strong Van der Waals was hailed enough to enter the liquid phase. At a liquid oxygen plant, oxygen immediately as one of the Hydrogen bonds are the strongest, gas is extracted from air in separation leading physicists of the day, which is why water has an unusually columns and cooled by passing through and in 1876 became Professor high boiling point for a substance heat exchangers to its liquefying of Physics at the University of made of oxygen and hydrogen. temperature of -302.8°F (-186°C). Amsterdam. He remained there for the rest of his career, Critical discoveries until succeeded as professor In showing that the attraction by his son, also called forces between gas molecules were Johannes. In 1910, Van der not zero but could be forced, under Waals was awarded the Nobel pressure, into state-changing Prize in Physics “for his work bonds, van der Waals laid the on the equation of state for foundations for the understanding gases and liquids.” He died of how liquids change into gases in Amsterdam in 1923. Key works 1873 On the Continuity of the Gaseous and Liquid State 1880 Law of Corresponding States 1890 Theory of Binary Solutions

COLLIDING IBNILLIAARDBBOALLXS STHTAETDISETVIECLAOLPMMEENCHTAONFICS



106 THE DEVELOPMENT OF STATISTICAL MECHANICS IN CONTEXT A gas consists of a huge number of molecules. KEY FIGURE The molecules are moving at high speeds and in Ludwig Boltzmann infinitely varied directions. (1844–1906) It is impossible to calculate the movement of BEFORE any individual molecule. 1738 Daniel Bernoulli makes the first statistical analysis Statistical averages and mathematical probability of particle movement. can help us understand the movement of the sum of 1821 John Herapath gives molecules in a system. the first clear statement of kinetic theory. speculated that this might be in the 1640s. The accepted because air is composed of explanation was that air is made 1845 John Waterston particles that repel each other, of particles, which were thought calculates the average in the manner of a spring. Isaac at the time to be floating in an speed of gas molecules. Newton proved mathematically invisible substance called “ether.” that if the “springiness” of air—its 1859 James Clerk Maxwell pressure—comes from repulsion Inspired by the recent invention lays out his kinetic theory. of particles, then the repulsive force of the steam engine, Bernoulli must be inversely proportional proposed a radical new idea. He AFTER to the distances between the asked his readers to imagine a 1902 Willard Gibbs publishes particles. But Newton believed the first major textbook on that the particles were fixed in statistical mechanics. place, vibrating on the spot. 1905 Marian von Gases and heat We live submerged Smoluchowski and Albert Swiss mathematician Daniel at the bottom of Einstein demonstrate Bernoulli made the first serious an ocean of the Brownian motion as statistical proposal of the kinetic (movement) element air. mechanics in action. theory of gases in 1738. Prior to that date, scientists already knew Evangelista Torricelli T he idea that properties of that air exerted pressure—for matter—and in particular, instance, enough pressure to hold of gases—depend on the up a heavy column of mercury, behavior of atoms and molecules which had been demonstrated by is now accepted as scientific fact. Evangelista Torricelli’s barometer But this theory was slow to gain acceptance and remained a subject of bitter dispute, particularly in the 19th century. Several pioneers faced at best neglect and at worst derision, and it was a long time before the “kinetic theory”—the idea that heat is the rapid movement of molecules—was truly accepted. In the 17th century, Robert Boyle showed that air is elastic, and expands and contracts. He

See also: Kinetic energy and potential energy 54 ■ Fluids 76–79 ■ Heat engines ENERGY AND MATTER 107 90–93 ■ Entropy and the second law of thermodynamics 94–99 Brownian motion A well-constructed theory who would be forever remembered is in some respects in the Kelvin temperature scale) In 1827, Scottish botanist drew the same conclusion in 1848. Robert Brown described undoubtedly an artistic the random movement of production. A fine example is It was in 1821 that British pollen grains suspended physicist John Herapath gave the in water. Although he the famous kinetic theory. first clear statement of kinetic was not the first to notice Ernest Rutherford theory. Heat was still seen as a this phenomenon, he was the fluid and gases were considered first to study it in detail. More piston within a cylinder, which to be made of repelling particles, investigation showed that contained tiny, round particles as Newton had suggested. But the tiny to-and-fro movements zooming this way and that. Bernoulli Herapath rejected this idea, of pollen grains got faster argued that as the particles collided suggesting instead that gases are as the temperature of the with the piston, they created made of “mutually impinging atoms.” liquid increased. pressure. If the air was heated, the If such particles were infinitely particles would speed up, striking small, he reasoned, collisions would The existence of atoms the piston more often and pushing it increase as a gas was compressed, and molecules was still a up through the cylinder. His proposal so pressure would rise and heat matter of heated debate at summed up the kinetic theory of would be generated. Unfortunately, the start of the 20th century, gases and heat, but his ideas were Herapath’s work was rejected by but in 1905 Einstein argued forgotten because first the theory the Royal Society in London as that Brownian motion could that combustible materials contain a overly conceptual and unproven. be explained by invisible fire element called phlogiston, then atoms and molecules the caloric theory—that heat is a In 1845, the Royal Society bombarding the tiny but kind of fluid—held sway for the next also rejected a major paper on visible particles suspended 130 years, until Ludwig Boltzmann’s kinetic theory by Scotsman John in a liquid, causing them statistical analysis in 1868 banished Waterston, which used statistical to vibrate back and forth. A it for good. rules to explain how energy is year later, Polish physicist distributed among gas atoms and Marian Smoluchowski Heat and motion molecules. Waterston understood published a similar theory, There were other unrecognized that molecules do not all move at and in 1908 Frenchman pioneers, too, such as Russian the same speed, but travel at a Jean Baptiste Perrin conducted polymath Mikhail Lomonosov, who range of different speeds around a experiments that confirmed in 1745 argued that heat is a measure statistical average. Like Herapath this theory. of the motion of particles—that is, before him, Waterston’s important the kinetic theory of heat. He went contribution was neglected, and Brownian motion of particles in on to say that absolute zero would the only copy of his groundbreaking a fluid results from collisions with be reached when particles stopped work was lost by the Royal Society. fast-moving molecules of the fluid. moving, more than a century before It was rediscovered in 1891, but It was eventually explained using William Thomson (later Lord Kelvin, by this time Waterston had gone statistical mechanics. missing and was presumed to have drowned in a canal near his Edinburgh home. Messy universe Waterston’s work was especially significant because this was the first time that physics rejected the perfect clockwork of the Newtonian universe. Instead, Waterston was ❯❯

108 THE DEVELOPMENT OF STATISTICAL MECHANICS looking at values whose range was A gas molecule collides Point A Molecule so messy that they could only be repeatedly with other Molecule changes looked at in terms of statistical molecules, causing it to direction averages and probabilities, not change direction. The after collision certainties. Although Waterston’s molecule shown here has work was originally rejected, the 25 such collisions, and Point B idea of understanding gas and heat the average distance it in terms of high-speed movements travels between each of minute particles was at last collision is what Rudolf beginning to take hold. The work of Clausius called its “mean British physicists James Joule and free path.” Compare the William Thomson, German physicist shortest distance Rudolf Clausius, and others was between point A and showing that heat and mechanical point B with the distance movement are interchangeable actually traveled. forms of energy—rendering redundant the idea that heat is temperature, meaning that each of gas is in fact far less varied than some kind of “caloric fluid.” molecule collides with another this, making the statistical task of more than 8 billion times a second. It analyzing them far simpler. Molecular movement is the sheer tininess and frequency Joule had calculated the very high of these collisions that make a gas Boltzmann’s breakthrough speeds of gas molecules with some appear to be fluid and smooth, The key figure in the development accuracy in 1847, but assumed that rather than a raging sea. of the statistical analysis of moving they all moved at the same speed. molecules was Austrian physicist Ten years later, Clausius furthered Within a few years, James Ludwig Boltzmann. In major papers understanding with his proposition Clerk Maxwell provided such a solid in 1868 and 1877, Boltzmann of a “mean free path.” As he saw it, exposition of kinetic theory that it at developed Maxwell’s statistical molecules repeatedly collide and last became more widely accepted. approach into an entire branch of bounce off each other in different Significantly, in 1859, Maxwell science—statistical mechanics. directions. The mean free path is introduced the first-ever statistical Remarkably, this new discipline the average distance each molecule law in physics, the Maxwell allowed the properties of gases and travels before bumping into another. distribution, which shows the heat to be explained and predicted Clausius calculated this to be barely probable proportion of molecules in simple mechanical terms, such a millionth of a millimeter at ambient moving at a particular velocity in an as mass, momentum, and velocity. ideal gas. Maxwell also established These particles, although tiny, Available energy is that the rate of molecularcollisions behaved according to Newton’s the main object at stake corresponds to temperature—the laws of motion, and the variety more frequent the collisions are, in their movement is simply down in the struggle for the higher the temperature. In to chance. Heat, which had existence and the 1873, Maxwell estimated that previously been thought of as a evolution of the world. there are 19 trillion molecules in mysterious and intangible fluid Ludwig Boltzmann a cubic centimeter of gas in ideal known as “caloric,” could now conditions—not that far from the be understood as the high-speed modern estimate of 26.9 trillion. movement of particles—an entirely mechanical phenomenon. Maxwell also compared molecular analysis to the science of Boltzmann faced a particular population statistics, which divided challenge in testing his theory: people according to factors such as molecules are so innumerable and education, hair color, and build, and so tiny that making individual analyzed them in order to determine calculations would be impossible. average characteristics. Maxwell More significantly, their movements observed that the vast population vary hugely in speed, and infinitely of atoms in just a cubic centimeter

ENERGY AND MATTER 109 in direction. Boltzmann realized that Boltzmann called its “macrostate”— Let us have free the only way to investigate the idea remains stable. Boltzmann realized scope for all directions in a rigorous and practical way was that a macrostate can be calculated to employ the math of statistics and by averaging the microstates. of research; probability. He was forced to forego away with dogmatism, the certainties and precision of To average the microstates Newton’s clockwork world, and that make up the macrostate, either atomistic or enter into the far messier world Boltzmann had to assume that all anti-atomistic. of statistics and averages. microstates are equally probable. He justified this assumption with Ludwig Boltzmann Micro and macrostates what came to be known as the The law of conservation of energy “ergodic hypothesis”—that over Scientists now understand a very long period of time, any that the subatomic world can be states that the total energy (E) in dynamic system will, on average, explored through probabilities spend the same amount of time and averages, not just as a wayof an isolated volume of gas must be in each microstate. This idea of understanding or measuring it, but constant. However, the energy of things averaging out was vital to as a glimpse of its very reality—the individual molecules can vary. So, Boltzmann’s thinking. apparently solid world we live in is the energy of each molecule cannot essentially a sea of subatomic Statistical thermodynamics probabilities. Back in the 1870s, be E divided by the total number Boltzmann’s statistical approach however, Boltzmann faced dogged of molecules (E/N), 19 trillion, for has had huge ramifications. It has opposition to his ideas when he become the primary means of laid out the mathematical basics instance—as it would be if they understanding heat and energy, of thermodynamics. He wrote two all had the same energy. Instead, and made thermodynamics—the key papers on the second law of Boltzmann looked at the range of study of the relationships between thermodynamics (previously ❯❯ possible energies that individual heat and other forms of energy— molecules might have, considering a central pillar of physics. His factors including their position and approach also became a hugely velocity. Boltzmann called this valuable way of examining the range of energies a “microstate.” subatomic world, paving the way for the development of quantum As the atoms within each science, and it now underpins molecule interact, the microstate much of modern technology. changes many trillions of times every second, but the overall condition of the gas—its pressure, temperature, and volume, which Ludwig Boltzmann Born in Vienna in 1844, at the kinetic theory of gases and height of the Austro-Hungarian the mathematical basis of Empire, Ludwig Boltzmann thermodynamics in relation studied physics at the University to the probable movements of of Vienna and wrote his PhD atoms. His ideas brought him thesis on the kinetic theory of opponents, and he suffered gases. At the age of 25, he became from bouts of depression. He a professor at the University of committed suicide in 1906. Graz, and then took teaching posts at Vienna and Munich Key works before returning to Graz. In 1900, he moved to the University of 1871 Paper on Maxwell– Leipzig to escape his bitter Boltzmann distribution long-term rival, Ernst Mach. 1877 Paper on second law of thermodynamics and probability It was at Graz that Boltzmann (“On the Relationship between completed his work on statistical the Second Fundamental”) mechanics. He established the

110 THE DEVELOPMENT OF STATISTICAL MECHANICS developed by Rudolf Clausius, be used to show the average The St. Louis World’s Fair in William Thomson, and William speed of the molecules and also 1904 was the venue for a lecture by Rankine), which shows that to show the most probable speed. Boltzmann on applied mathematics. heat flows only in one direction, The distribution highlights the His American tour also included visits from hot to cold, not from cold to “equipartition” of energy—which to Stanford and Berkeley universities. hot. Boltzmann explained that shows that the energy of moving the law could be understood atoms averages out as the same The majority of scientists only precisely by applying both the in any direction. accepted the existence of atoms basic laws of mechanics (that is, after contributions from Albert Newton’s laws of motion) and Atomic denial Einstein and Polish physicist the theory of probability to the Boltzmann’s approach was Marian Smoluchowski. Working movement of atoms. such a novel concept that he independently, they explored faced fierce opposition from Brownian motion, the unexplained In other words, the second law some of his contemporaries. random flitting to and fro of tiny, of thermodynamics is a statistical Many considered his ideas suspended particles in a fluid. In law. It states that a system tends to be fanciful, and it is possible 1905, Einstein, and the following toward equilibrium, or maximum that hostility to his work year, Smoluchowski, both showed entropy—the state of a physical contributed to his eventual that it could be explained via system at greatest disorder— suicide. One reason for such statistical mechanics as the result because this is by far the most opposition was that many of collisions of the particles with probable outcome of atomic scientists at the time were the fast-moving molecules of the motion; things average out over unconvinced of the existence fluid itself. time. By 1871, Boltzmann had of atoms. Some, including Austrian also developed Maxwell’s physicist Ernst Mach—a fierce Wider acceptance distribution law of 1859 into a rival to Boltzmann, and known Although a brilliant lecturer who rule that defines the distribution for his work on shock waves— was much loved by his students, of speeds of molecules for a gas believed that scientists should Boltzmann did not achieve wider at a certain temperature. The only accept what they could popularity for his work, perhaps resulting Maxwell–Boltzmann directly observe, and atoms because he did not promote it. distribution is central to the could not be seen at the time. The widespread acceptance of his kinetic theory of gases. It can theoretical approach was due in some part to American physicist PROPORTION OF MOLECULES 0.004 This Maxwell–Boltzmann distribution 0.003 shows the speeds of molecules (the distribution of 0.002 probabilities of gas molecules moving at a certain 0.001 speed) for helium, neon, argon, and xenon, at a temperature of 77 ºF (25 ºC). On average, heavier molecules—such as xenon—move more slowly than lighter molecules, such as helium. This means that heavier molecules have a narrower speed distribution, whereas lighter molecules have a speed distribution that is spread out more widely. Xenon Neon Argon Helium 0 500 1000 1500 2000 2500 SPEED (METERS/SECOND)

Willard Gibbs, who wrote the first Atoms? ENERGY AND MATTER 111 major textbook on the subject, Have you Statistical Mechanics, in 1902. seen one yet? Weather forecasts Ernst Mach It was Gibbs who coined the The methods developed phrase “statistical mechanics” matter, and all complex things, are in statistical mechanics to to encapsulate the study of the subject to probability and entropy. analyze and predict mass mechanical movement of particles. It is impossible to overestimate movements of particles have He also introduced the idea of an the immense shift in outlook his been used in many situations “ensemble,” a set of comparable ideas created among physicists. beyond thermodynamics. microstates that combine to form a The certainties of Newtonian similar macrostate. This became physics had been replaced by a One real-world application, a core idea in thermodynamics, view of the universe in which there for instance, is the calculation and it also has applications in is only a fizzing sea of probabilities, of “ensemble” weather other areas of science, ranging and the only certainties are forecasts. More conventional from the study of neural pathways decay and disorder. ■ methods of numerical weather to weather forecasting. forecasting involve collecting A tornado is a chaotic system that data from weather stations Final vindication can be analyzed using statistical and instruments around the Thanks to Gibbs, Boltzmann mechanics. Projecting the distribution world and using it to simulate was invited on a lecture tour in of atmospheric molecules can help future weather conditions. In the US in 1904. By that time, the gauge its temperature and intensity. contrast, ensemble forecasting hostility to his life’s work was is based on a large number beginning to take its toll. He had a of possible future weather medical history of bipolar disorder, predictions, rather than on and in 1906 he hanged himself a single predicted outcome. while on a family vacation in The probability that a single Trieste, Italy. In a bitter twist of forecast will be wrong is fate, his death came in the same relatively high, but forecasters year that the work of Einstein can have a strong degree of and Smoluchowski was gaining confidence that the weather acceptance, vindicating Boltzmann. will fall within a given range His overarching idea was that of an ensemble forecast. The idea was proposed by American mathematician Edward Lorenz in a 1963 paper, which also outlined “chaos theory.” Known for the so-called “butterfly effect,” his theory explored how events occur in a chaotic system such as Earth’s atmosphere. Lorenz famously suggested that a butterfly flapping its wings can set off a chain of events that eventually triggers a hurricane. The power of a statistical approach is immense, and allowing uncertainty to play a part has enabled weather forecasting to become far more reliable. Forecasters can confidently predict weather locally for weeks in advance— within a given range.

GOLDFETCHING SOME FROM THE SUN THERMAL RADIATION



114 THERMAL RADIATION IN CONTEXT A material that absorbs energy at a certain wavelength emits energy at the KEY FIGURE Gustav Kirchhoff same wavelength. (1824–1887) A blackbody absorbs all the energy that strikes it. The energy of radiation emitted by a blackbody BEFORE 1798 Benjamin Thompson depends only on its temperature. (Count Rumford) suggests When the blackbody is in equilibrium with its that heat is related to motion. surroundings, the radiation absorbed equals 1844 James Joule argues the radiation emitted. that heat is a form of energy and that other forms of energy can be converted to heat. 1848 William Thomson (Lord Kelvin) defines absolute zero. AFTER 1900 German physicist Max Planck proposes a new theory for blackbody radiation, and introduces the idea of the quantum of energy. 1905 Albert Einstein uses Planck’s idea of blackbody radiation to solve the problem of the photoelectric effect. H eat energy can be his theory was correct. Everything light. In 1800, he used a prism transferred from one place that has a temperature above to split light into a spectrum, to another in one of three absolute zero (equal to –459.67 °F and measured the temperature ways: by conduction in solids, by or –273.15 °C) emits radiation. at different points within that convection in liquids and gases, All of the objects in the universe spectrum. He noticed that and by radiation. This radiation, are exchanging electromagnetic the temperature increased known as thermal—or heat— radiation with each other all of as he moved his thermometer radiation, does not require the time. This constant flow of from the violet part of the spectrum physical contact. Along with radio energy from one object to another to the red part of the spectrum. waves, visible light, and X-rays, prevents anything from cooling thermal radiation is a form of to absolute zero, the theoretical To his surprise, Herschel found electromagnetic radiation that minimum of temperature at that the temperature also increased travels in waves through space. which an object would transmit beyond the red end of the spectrum, no energy at all. where no light was visible at James Clerk Maxwell was the all. He had discovered infrared first to propose the existence of Heat and light radiation—a type of energy that electromagnetic waves in 1865. German-born British astronomer is invisible to the eye, but which He predicted that there would William Herschel was one of can be detected as heat. For be a whole range, or spectrum, the first scientists to observe a example, modern-day toasters use of electromagnetic waves, and connection between heat and infrared radiation to transmit heat later experiments showed that energy to the bread.

ENERGY AND MATTER 115 See also: The conservation of energy 55 ■ Heat and transfers 80–81 ■ Internal energy and the first law of thermodynamics 86–89 ■ Heat engines 90–93 ■ Electromagnetic waves 192–195 ■ Energy quanta 208–211 The amount of thermal radiation Intensely cold gas and dust in the Bodies can be imagined given off by an object depends on Eagle nebula are rendered in reds which … completely absorb its temperature. The hotter the (–442 ˚F or –263 ˚C) and blues (–388 ˚F all incident rays, and neither object, the more energy it emits. or –205 ˚C) by the Herschel Space If an object is hot enough, a large Observatory far-infrared telescope. reflect nor transmit any. portion of the radiation it emits I shall call such bodies … can be seen as visible light. For temperature of more than 1,292 °F example, a metal rod heated to a (700 °C). Objects with equal blackbodies. high enough temperature will radiative properties emit light Gustav Kirchhoff begin to glow first a dull red, then of the same color when they yellow, then brilliant white. A metal reach the same temperature. Two years after Stewart’s paper rod glows red when it reaches a was published, German physicist Absorption equals emission Gustav Kirchhoff, unaware of the In 1858, Scottish physicist Balfour Scotsman’s work, published Stewart presented a paper titled “An similar conclusions. At the time, Account of Some Experiments on the academic community judged Radiant Heat.” While investigating that Kirchhoff’s work was more the absorption and emission of heat rigorous than Stewart’s in thin plates of different materials, investigations, and found more he found that at all temperatures, immediate applications to other the wavelengths of absorbed fields, such as astronomy. Despite and emitted radiation are equal. his discovery being the earlier ❯❯ A material that tends to absorb energy at a certain wavelength tends also to emit energy at that same wavelength. Stewart noted that “the absorption of a plate equals its radiation [emission], and that for every description [wavelength] of heat.” Gustav Kirchhoff Born in 1824, Kirchhoff was that each chemical element educated in Königsberg, Prussia has a unique, characteristic (modern-day Kaliningrad, Russia). spectrum. He then worked He proved his mathematical skill with Robert Bunsen in 1861 in 1845 as a student, by extending to identify the elements in the Ohm’s law of electrical current sun’s atmosphere by examining into a formula that allowed the its spectrum. calculation of currents, voltages, and resistances in electrical Although poor health in later circuits. In 1857, he discovered life prevented Kirchhoff from that the velocity of electricity in a laboratory work, he continued to highly conductive wire was almost teach. He died in Berlin in 1887. exactly equal to the velocity of light, but he dismissed this as a Key work coincidence, rather than inferring that light was an electromagnetic 1876 Vorlesungen über phenomenon. In 1860, he showed mathematische Physik (Lectures on mathematical physics)

116 THERMAL RADIATION Since we can produce example, has its peak at the center radiation that is absorbed by the all types of light by means of the visible light range. Since surface is equal to the amount of hot bodies, we can ascribe, perfect blackbodies do not exist, to emitted, at any temperature and to the radiation in thermal help explain his theory Kirchhoff wavelength. Hence, the efficiency equilibrium with hot bodies, conjectured a hollow container with with which an object absorbs a single, tiny hole. Radiation can radiation at a given wavelength the temperature of only enter the container through the is the same as the efficiency with these bodies. hole, and is then absorbed inside which it emits energy at that the cavity, so the hole acts as a wavelength. This can be expressed Wilhelm Wien perfect absorber. Some radiation more concisely as: absorptivity will be emitted through the hole equals emissivity. of the two, Stewart’s contribution and through the surface of the to the theory of thermal radiation cavity. Kirchhoff proved that the In 1893, German physicist was largely forgotten. radiation inside the cavity depends Wilhelm Wien discovered the only on the temperature of the mathematical relationship between Blackbody radiation object, and not on its shape, size, temperature change and the shape Kirchhoff’s findings can be or the material it is made from. of the blackbody curve. He found explained as follows. Imagine an that when the wavelength at which object that perfectly absorbs all of Law of thermal radiation the maximum amount of radiation the electromagnetic radiation that Kirchhoff’s 1860 law of thermal is emitted was multiplied by the strikes it. Since no radiation is radiation states that when an object temperature of the blackbody, the reflected from it, all of the energy is in thermodynamic equilibrium— resulting value is always a constant. that it emits depends solely on its at the same temperature as the temperature, and not its chemical objects around it—the amount of This finding meant that composition or physical shape. the peak wavelength could be In 1862, Kirchhoff coined the calculated for any temperature, term “blackbodies” to describe these hypothetical objects. Perfect Blackbody curves depict the radiation blackbodies do not exist in nature. emitted by objects at different wavelengths of the electromagnetic spectrum. The An ideal blackbody absorbs approximated curves on this graph show and emits energy with 100 percent RADIATION EMISSION objects at four different temperatures, and efficiency. Most of its energy output Ultraviolet are roughly equivalent to the sun, Aldebaran is concentrated around a peak Visible (a red-giant star), a carbon-arc electric lamp, frequency—denoted  max, where 10 Infrared and a halogen light bulb.  is the wavelength of the radiation emitted—which increases as the 8 temperature increases. When plotted on a graph, the spread T = 6000 °K (sun) T = 4000 °K (carbon- of energy-emitting wavelengths arc electric lamp) around the object’s peak frequency takes a distinctive profile known 6 T = 5000 °K T = 3000 °K (halogen as a “blackbody curve.” The (Aldebaran) light bulb) blackbody curve of the sun, for T = temperature 4 K = kelvins = MAX 2 0 1.0 2.0 WAVELENGTH () MEASURED IN MICROMETERS

incorrect. But explaining why the ENERGY AND MATTER 117 Rayleigh–Jeans calculations were wrong required bold theoretical Stellar temperatures physics, the likes of which had never been attempted. It is possible to calculate the surface temperature of a Kirchhoff envisaged a blackbody as Quantum beginnings blackbody by measuring the a container with a small hole. Most of At the same time as the Rayleigh– energy that it emits at specific the radiation that enters the enclosure Jeans findings were announced, wavelengths. Since stars, will be trapped. The amount of radiation Max Planck was working on his including the sun, produce emitted depends on the surroundings. own theory of blackbody radiation light spectrums that closely in Berlin. In October 1900, he approximate a blackbody and it explained why objects proposed an explanation for the spectrum, it is possible to change color as they get hotter. blackbody curve that agreed calculate the temperature of As the temperature increases with all the known experimental a distant star. the peak wavelength decreases, measurements, yet went beyond moving from longer infrared waves the framework of classical physics. A blackbody’s temperature to shorter ultraviolet waves. By His solution was radical, and is given by the following 1899, however, careful experiments involved an entirely new way showed that Wien’s predictions of looking at the world. Tformula: = 2898 ∕  max were not accurate for wavelengths where T = the temperature in the infrared range. Planck found that the ultraviolet catastrophe could be averted by of the blackbody (measured Ultraviolet catastrophe understanding a blackbody’s in degrees Kelvin), and  max = In 1900, British physicists Lord energy emission as occurring the wavelength (, measured Rayleigh and Sir James Jeans not in continuous waves, but in in micrometers) of the published a formula that seemed discrete packets, which he called maximum emission of the to explain what had been observed “quanta.” On December 19, 1900, blackbody. at the infrared end of the spectrum. Planck presented his findings to However, their findings were soon a meeting of the German Physical This formula can be used called into question. According to Society in Berlin. This date is to calculate the temperature their theory, there was effectively generally accepted as marking of a star’s photosphere—the no upper limit to the higher the birth of quantum mechanics, light-emitting surface—using frequencies of ultraviolet energy and a new era in physics. ■ the wavelength at which it that would be generated by the emits the maximum amount blackbody radiation, meaning These laws of light … of light. Cool stars emit more that an infinite number of highly may have been observed light from the red and orange energetic waves would be before, but I think they end of the spectrum, whereas produced. If this was the case, are now for the first time hotter stars appear blue. For opening the oven door to check connected with a theory instance, blue supergiants—as on a cake as it bakes would result depicted in the above artist’s in instant annihilation in a burst of radiation. impression—are a class of star of intense radiation. This came Gustav Kirchhoff that can be up to eight times to be known as the “ultraviolet hotter than the sun. catastrophe,” and was obviously

EMLAEGCNTERTIICSI two forces unite

MTY AND

120 INTRODUCTION The ancient Greeks English physician and physicist Benjamin Franklin Alessandro Volta give amber an electric William Gilbert publishes De develops his one-fluid demonstrates the theory of electricity, in first electric pile, or charge by rubbing it Magnete (On the Magnet), the first battery, which with rabbit fur, using systematic work on electricity and which he introduces provides continuous its attraction to move the idea of positive electric current for magnetism since antiquity. He and negative charge. light objects. coins the new Latin word electrica, the first time. from the Greek for amber (elektron). 6TH CENTURY BCE 1600 1747 1800 1785 2ND CENTURY BCE 1745 Chinese scholars use German cleric Ewald Georg Charles-Augustin de Coulomb shards of magnetic von Kleist and Dutch scientist discovers his law for lodestone as simple Pieter van Musschenbroek determining the attractive or direction-finders. invent the Leyden jar as a way repulsive force between two of storing electric charge. electrically charged objects. I n ancient Greece, scholars force producing these phenomena together produced behavior noticed that some stones from was evidence that the stones and similar to that of amber and fur. Magnesia, in modern-day amber had a soul. For example, glass rubbed with Thessaly, behaved strangely when silk also made small objects dance. they were placed near certain The strange forces exhibited by When both amber and glass were metals and iron-rich stones. The the stones from Magnesia are today rubbed, they pulled together in stones pulled metals toward known as magnetism, taking its an attraction, while two lumps of them through an unseen attraction. name from the region where it was amber or two of glass would push When placed in a particular way, first found. Forces exhibited by apart. These were identified as two of these stones were seen to the amber were given the name two distinct electricities—vitreous attract each other, but they pushed electricity from the ancient Greek electricity for the glass and each other apart when one was word for amber, elektron. Chinese resinous for the amber. flipped around. scholars and, later, mariners and other travelers used small shards American polymath Benjamin Ancient Greek scholars also of magnesia stone placed in Franklin chose to identify these noted a similar, but subtly different, water as an early version of two types of electricity with behavior when amber (fossilized the compass, since the stones positive or negative numbers, with tree sap) was rubbed with animal aligned themselves north–south. a magnitude that became known fur. After rubbing for a little time, as electric charge. While hiding the amber would gain a strange Attraction and repulsion from the revolutionists to keep his ability to make light objects, such No new use was found for head attached to his body, French as feathers, ground pepper, or hair, electricity until the 18th century. By physicist and engineer Charles- dance. The mathematician Thales this time, it had been discovered Augustin de Coulomb carried of Miletus argued that the unseen that rubbing other materials out a series of experiments.

ELECTRICITY AND MAGNETISM 121 French physicist André-Marie Michael Faraday American inventor American chemist Ampère provides a generates an Thomas Edison’s Chad Mirkin invents first electricity nanolithography, mathematical derivation of electric current generating plant the magnetic force between from a changing starts producing which “writes” two parallel wires carrying an magnetic field to nanocircuitry on discover induction. in London. silicon wafers. electric current. 1825 1831 1882 1999 1911 1820 1827 1865 Danish physicist Hans German physicist Georg James Clerk Dutch physicist Christian Ørsted Ohm publishes his law Maxwell combines Heike Kamerlingh Onnes discovers discovers that a wire establishing the all knowledge of superconductivity in carrying an electric relationship between electricity and magnetism mercury chilled to current produces a near absolute zero. current, voltage, in a few equations. magnetic field. and resistance. He discovered that the force of to an electric potential difference. Maxwell elegantly accommodated attraction or repulsion between We now know that chemical Faraday’s findings, and those electric objects grew weaker as the reactions and the flow of electricity of earlier scientists, in just four distance between them increased. through a metal are inextricably equations. In doing so, he linked because both result from the discovered that light was a Electricity was also observed movement of subatomic electrons. disturbance in electric and to flow. Small sparks would leap magnetic fields. Faraday conducted from an electrically charged A combined force experiments that demonstrated object to one without charge in In mid-19th-century Britain, Michael this, showing that magnetic fields an attempt to balance out, or Faraday and James Clerk Maxwell affect the behavior of light. neutralize charge. If one object produced the link between the was at a different charge from those two apparently distinct forces of Physicists’ understanding surrounding it, then that object was electricity and magnetism, giving of electromagnetism has said to have different potential. Any rise to the combined force of revolutionized the modern world difference in potential can induce a electromagnetism. Faraday created through technologies that have flow of electricity called a current. the idea of fields, lines of influence been developed to use electricity Electric currents were found to flow that stretch out from an electric and magnetism in new and easily through most metals, while charge or magnet, showing the innovative ways. Research into organic materials seemed far less region where electric and magnetic electromagnetism also opened able to permit a current to flow. forces are felt. He also showed that up previously unthought-of areas moving magnetic fields can induce of study, striking at the heart of In 1800, Italian physicist an electric current and that electric fundamental science—guiding us Alessandro Volta noticed that currents produce magnetic fields. deep inside the atom and far out differences in the chemical into the cosmos. ■ reactivity of metals could lead

122 FWOORNCDERSOUS MAGNETISM IN CONTEXT T he striking properties of would inherit its properties and the rare, naturally occurring could be used to make a compass. KEY FIGURE lodestone—an ore of iron The maritime compass made it William Gilbert (1544–1603) called magnetite—fascinated possible for ships to navigate away ancient cultures in Greece from the shore, and the instrument BEFORE and China. Early writings from reached Europe via Chinese 6th century bce Thales of these civilizations describe seafarers. By the 16th century, Miletus states iron is attracted how lodestone attracts iron, the compass was driving the to the “soul” of lodestone. affecting it over a distance expansion of European empires, without any visible mechanism. as well as being used in land 1086 Astronomer Shen Kuo surveying and mining. (Meng Xi Weng) describes a By the 11th century, the Chinese magnetic needle compass. had discovered that a lodestone Despite centuries of practical would orient itself north–south if application, the underlying physical 1269 French scholar Petrus allowed to move freely (for example, mechanism of magnetism was Peregrinus describes magnetic when placed in a vessel floating in poorly understood. The first poles and laws of attraction a bowl of water). Moreover, an iron systematic account on magnetism and repulsion. needle rubbed with lodestone was Petrus Peregrinus’ 13th-century AFTER A compass needle points approximately north, but also 1820 Hans Christian Ørsted shows declination (deviation away from true north) and discovers that an electric inclination (tilting toward or away from Earth’s surface). current flowing in a wire deflects a magnetic needle. A compass needle shows exactly the same behavior when moved over the surface of a 1831 Michael Faraday describes invisible “lines of spherical magnetic rock, or lodestone. force” around a magnet. Earth is a giant magnet. 1906 French physicist Pierre- Ernest Weiss advances the theory of magnetic domains to explain ferromagnetism.

ELECTRICITY AND MAGNETISM 123 See also: Making magnets 134–135 ■ The motor effect 136–137 ■ Induction and the generator effect 138–141 ■ Magnetic monopoles 159 The poles of iron bars are When a magnet is brought close to William Gilbert changed when a lodestone an object made from ferromagnetic simply presents its pole to material, the object itself becomes William Gilbert was born into them and faces them even magnetic. The approaching pole a prosperous English family in of the magnet induces an opposite 1544. After graduating from from some distance. pole in the near side of the Cambridge, he established William Gilbert ferromagnetic object and attracts it. himself as a leading physician Depending on its exact composition in London. He met prominent text in which he described polarity and interaction with the magnet, naval officers, including (the existence of magnetic north the ferromagnetic object may Francis Drake, and cultivated and south poles in pairs). He also become permanently magnetized, connections at the court of found that pieces of a lodestone retaining this property after the Elizabeth I. Through his “inherited” magnetic properties. original magnet is removed. connections and on visits to the docks, Gilbert learned Gilbert’s little Earths Once physicists connected of the behavior of compasses It was English astronomer William electricity and magnetism and at sea and acquired specimens Gilbert’s groundbreaking work that developed an understanding of of lodestones. His work with dispelled long-held superstitions atomic structure in the 19th these magnetic rocks informed about magnetism. Gilbert’s key century, a reasonable theory of his masterwork. innovation was to simulate nature ferromagnetism began to emerge. in the laboratory. In 1600, Gilbert was The idea is that the movement elected president of the Royal Using spheres of lodestone of electrons in an atom makes each Society of Physicians and that he called terella (Latin for little atom into a miniature magnetic appointed personal physician Earths), he showed that a compass dipole (with north and south poles). to Elizabeth I. He also needle was deflected in the same In ferromagnetic materials such as invented the electroscope to way over different parts of the iron, groups of neighboring atoms detect electric charge and sphere as it was over the align to form regions called distinguished the force of corresponding regions of our magnetic domains. static electricity from that of planet. He concluded that Earth magnetism. He died in 1603, was itself a giant magnet and These domains are usually possibly succumbing to published his findings in the arranged in closed loops, but when bubonic plague. groundbreaking De Magnete a piece of iron is magnetized, the (On the Magnet) in 1600. domains line up along a single axis, Key works creating north and south poles at opposite ends of the piece. ■ 1600 De Magnete (On the Magnet) A new understanding A simple magnet, with a north and 1651 De Mundo nostro The magnetism exhibited by south pole, creates lines of force around Sublunari Philosophia Nova magnetite is called ferromagnetism, it. Iron filings scattered around the (The New Philosophy) a property that is also seen with magnet line up along these lines of iron, cobalt, nickel, and their alloys. force, which is stronger at each pole.

124 IN CONTEXT OTHFEELAETCTTRRAICCTIITOYN KEY FIGURE Charles-Augustin de ELECTRIC CHARGE Coulomb (1736–1806) BEFORE 6th century bce Thales of Miletus notes electrostatic effects caused by friction in elektron (Greek for amber). 1747 Benjamin Franklin identifies positive and negative charge. AFTER 1832 Michael Faraday shows static and current electrical effects are manifestations of a single phenomenon. 1891 George J. Stoney says charge occurs in discrete units. 1897 J.J. Thomson finds that cathode rays are streams of charged subatomic particles. 1909 Robert Millikan studies the charge on an electron. F or millennia, people have observed electrical effects in nature—for example, lightning strikes, the shocks delivered by electric rays (torpedo fish), and the attractive forces when certain materials touch or are rubbed against each other. However, it is only in the last few hundred years that we have begun to understand these effects as manifestations of the same underlying phenomenon— electricity. More precisely, these are electrostatic effects, due to electric forces arising from static (stationary) electric charges. Electric current effects, on the other hand, are caused by moving charges.

ELECTRICITY AND MAGNETISM 125 See also: Laws of gravity 46–51 ■ Electric potential 128–129 ■ Electric current and resistance 130–133 ■ Bioelectricity 156 ■ Subatomic particles 242–243 Negatively as well as attractive, and Electrostatic charged postulated that there were two discharge comb types of electrical fluid—vitreous and resinous. Like fluids (such as An electrostatic discharge Metal plate two vitreous fluids) repelled each occurs when the electric other, and unlike fluids attracted. charge carriers (typically Metal rod electrons) in a charged body This theory was simplified by or region are rapidly and Gold foil leaves American statesman and polymath violently conducted away from move apart Benjamin Franklin in 1747, when he it. Lightning is a particularly proposed that there was only one powerful form of electrostatic The gold-leaf electroscope detects type of electrical fluid and different discharge that occurs when static electricity through the principle objects could have a surplus or so much charge has built up of like charges repelling. When a deficiency of this fluid. He labeled a between regions of the negatively charged comb is brought surplus of fluid (charge, in today’s atmosphere that the near the metal plate, electrons (which terms) to be positive, and a deficit intervening space becomes carry negative charge) are repelled negative, and proposed that the ionized (electrons separate toward the electroscope’s gold foil total amount of fluid in the universe from their atoms) and can leaves, which causes the leaves was conserved (constant). He also conduct a current. to separate. designed (and possibly conducted) an experiment to show that lightning The current is made visible The concept of electric charge, and was a flow of electrical fluid, by by the electrons heating up a mathematical description of the flying a kite in a storm. Charge is the air so much that it emits forces between charges, emerged still labeled as positive or negative, light. Ionization occurs over in the 18th century. Previously, the although this is simply convention: short distances, which is why ancient Greeks had noted that there is no excess “fluid” in a proton lightning bolts appear forked, when a piece of amber (elektron), that makes it positive, and nothing changing direction every was rubbed with wool, it would lacking in an electron that makes few feet. Electrostatic attract light objects such as feathers. it negative. discharge happens first at sharp edges—which is why In his 1600 book De Magnete Coulomb’s law your hair stands on end when (On the Magnet), William Gilbert During the 18th century, scientists statically charged (the hair named this effect “electricus” and suggested mathematical laws that tips repel each other) and discussed his experiments with the might govern the strength of the ❯❯ why lightning conductors and instrument that he had devised to static discharge devices on detect the force—the versorium. Bodies, electrified with the aircraft wings are shaped Gilbert saw that the force had an same kind of electricity, are like spikes. instantaneous effect over distance and suggested that it must be mutually repelled. carried by a fast-moving electrical Charles-Augustin de “fluid” released by the rubbed amber, rather than a slowly diffusing Coulomb “effluvium,” as previously thought. In 1733, French chemist Charles François du Fay observed that electrical forces could be repulsive

126 ELECTRIC CHARGE electrical force, modeled on the Two electrically charged A torsion balance can inverse square law of gravitation bodies experience a small measure the force by how that Newton had established in his much it twists a silk thread. hugely influential Principia of 1687. mutual force. In 1785, French engineer When the distance between the charged Charles-Augustin de Coulomb bodies is doubled, the amount of torsion (twisting) is developed a torsion balance that was sensitive enough to measure reduced to a quarter of the original. the electrical force between charges. The apparatus consisted The electrical force between charged bodies varies inversely of a series of metal spheres with the square of the distance between them. connected by a rod, needle, and silk thread. When Coulomb held a Coulomb established that when was quantized—and in 1891, charged object next to the external electric charges attract or repel he suggested a name for this sphere, the charge transferred to an each other, there is a relationship unit—the electron. internal sphere and needle. The between the strength of attraction needle, suspended from a silk or repulsion and distance. However, In 1897, British physicist thread, moved away from the it would be more than a century J.J. Thomson demonstrated that charged sphere and produced a before scientists came closer to cathode rays—the glowing “rays” twisting (torsion) in the silk thread. understanding the exact nature of electricity that could be made to The degree of torsion could be of electric charge. travel between two charged plates measured from a scale. in a sealed glass tube containing Finding the charge carrier very little gas (a near vacuum)— Coulomb published a series of In the 1830s, British scientist were in fact made of electrically papers detailing his experiments Michael Faraday carried out charged particles. By applying and establishing that the force experiments with electrolysis electric and magnetic forces of between two stationary, charged (using electricity to drive chemical known strength to the cathode bodies was inversely proportional reactions) and found that he rays, Thomson could bend them to the distance between them. He needed a specific amount of by a measurable amount. He could also assumed, but did not prove, electricity to create a specific then calculate how much charge a that the force was proportional to amount of a compound or element. particle must carry per unit mass. the product of the charges on the Although he was not convinced bodies. Today, this law is called that matter was made up of atoms Thomson also deduced that Coulomb’s law. (indivisible parts), this result these charge carriers were very suggested that electricity, at least, much lighter than the smallest The sciences are monuments might come in “packets.” In 1874, atom. They were common in all devoted to the public good; Irish physicist George Stoney matter because the behavior of each citizen owes to them developed the idea that there was the rays did not vary even if he an indivisible packet or unit of used plates of different metals. a tribute proportional to electric charge—that is, charge This subatomic particle—the his talents. first to be discovered—was then given Stoney’s name for the basic Charles-Augustin de Coulomb

ELECTRICITY AND MAGNETISM 127 unit of charge: the electron. The be 1.6  10-19 C (coulombs), very one percent would make it feel charge on an electron was assigned close to today’s accepted value. forces of devastating power. Our as negative. The discovery of the Nearly a century after Franklin understanding of electric charge positive charge carrier, the proton, suggested that the total amount and carriers has not changed would follow a few years later. of electric “fluid” is constant, dramatically since the discovery Faraday conducted experiments of the electron and proton. We also The charge on an electron that suggested that charge is know of other charge carriers, such Although Thomson had calculated conserved—the total amount as the positively charged positron the charge-to-mass ratio for the of charge in the universe remains and the negatively charged electron, neither the charge nor the the same. antiproton that make up an exotic mass were known. From 1909 to form of matter called antimatter. 1913, American physicist Robert Balance of charge Millikan performed a series of This principle of conservation of In modern terminology, electric experiments to find these values. charge is a fundamental one in charge is a fundamental property Using special apparatus, he modern physics, although there are of matter that occurs everywhere— measured the electric field needed circumstances—in high-energy in lightning, inside the bodies of to keep a charged droplet of oil collisions between particles in electric rays, in stars, and inside us. suspended in air. From the radius particle accelerators, for example— Static charges create electric fields of a droplet, he could work out its where charge is created through a around them—regions in which weight. When the droplet was still, neutral particle splitting into other electric charges “feel” a force. the upward electric force on it negative and positive particles. Moving charges create electric and balanced the downward However, in this case, the net magnetic fields, and through the gravitational force, and the charge charge is constant—equal numbers subtle interplay between these on the droplet could be calculated. of positive and negative particles fields, give rise to electromagnetic carrying equal amounts of negative radiation, or light. By repeating the experiment and positive charge are created. many times, Millikan discovered Since the development of that droplets all carried charges that This balance between charges quantum mechanics and particle were whole-number multiples of a isn’t surprising given the strength physics in the 20th century, we particular smallest number. Millikan of the electric force. The human now understand that many of the reasoned that this smallest number body has no net charge and most familiar properties of matter must be the charge on a single contains equal amounts of are fundamentally connected electron—called the elementary positive and negative charge, but to electromagnetism. Indeed, the charge, e—which he computed to a hypothetical imbalance of just electromagnetic force is one of the fundamental forces of nature. ■ Charles-Augustin de Born in 1736 into a relatively he formulated the inverse square Coulomb wealthy French family, Coulomb law that bears his name. He also graduated as a military engineer. consulted on civil engineering He spent nine years in the French projects and oversaw the colony of Martinique in the West establishment of secondary Indies but was dogged by illness schools. He died in Paris in and returned to France in 1773. 1806. The SI unit of charge, the coulomb, is named in his honor. While building a wooden fort in Rochefort, southwestern Key works France, he conducted pioneering work on friction and won the 1784 Theoretical Research and Grand Prize of the Académie des Experiments on the Torsion Force Sciences in 1781. He then moved and Elasticity of Metal Wires to Paris and devoted most of his 1785 Memoirs on Electricity and time to research. As well as Magnetism developing the torsion balance, Coulomb wrote memoirs in which

128 PBMOEOTCTEOIONMNTEIASLPEANLEPRAGBYLE ELECTRIC POTENTIAL IN CONTEXT T hrough the 17th and 18th electrochemical cell, that scientists centuries, an increasing had a supply of a moderate flow of KEY FIGURE number of investigators electrical charge over time: a current. Alessandro Volta began to apply themselves to (1745–1827) studying electricity, but it remained Energy and potential an ephemeral phenomenon. Both the sudden discharge of BEFORE the Leyden jar and the extended 1745 Pieter van The Leyden jar, invented in 1745 discharge (current) from a battery Musschenbroek and E. Georg by two Dutch and German chemists are caused by a difference in what is von Kleist invent the Leyden working independently, allowed called “electric potential” between jar, the first practical device electric charge to be accumulated each device and its surroundings. that can store electric charge. and stored until it was needed. However, the jar would discharge Today, electric potential is 1780 Luigi Galvani observes (unload the charge) rapidly as a considered to be a property of “animal electricity.” spark. It was not until the late the electric field that exists around 18th century, when Italian chemist electric charges. The electric AFTER Alessandro Volta developed the first potential at a single point is always 1813 French mathematician and physicist Siméon-Denis In a gravitational field, Similarly, an imbalance of Poisson establishes a general different altitudes have charge between different equation for potential. places in an electric field different amounts of gives these places different 1828 British mathematician gravitational potential. George Green develops amounts of electric Poisson’s ideas and introduces potential. the term “potential.” A difference in altitude A difference in electric 1834 Michael Faraday causes a current of water potential causes a current explains the chemical basis of the voltaic (galvanic) cell. to flow. of electricity to flow. 1836 British chemist John Daniell invents the Daniell cell.

ELECTRICITY AND MAGNETISM 129 See also: Kinetic energy and potential energy 54 ■ Electric charge 124–127 ■ Electric current and resistance 130–133 ■ Bioelectricity 156 measured relative to that at another apart the opposite poles of two Alessandro Volta point. An imbalance of charge magnets does). This energy comes between two points gives rise from chemical reactions in the cell. Alessandro Volta was born to a potential difference between When the cell is connected to an into an aristocratic family in them. Potential difference is external circuit, the energy that was 1745 in Como, Italy. Volta was measured in volts (V) in honor of “stored” in the potential difference just seven years old when his Volta, and is informally referred to appears as the electrical energy that father died. His relatives as “voltage.” Volta’s work paved the drives the current around the circuit. steered his education toward way for fundamental breakthroughs the Church, but he undertook in the understanding of electricity. Volta made his battery by his own studies in electricity connecting individual cells made of and communicated his ideas From animal electricity silver and zinc disks separated by to prominent scientists. to batteries brine-soaked cloth. He demonstrated In 1780, Italian physician Luigi the resulting voltaic pile to the Following Volta’s early Galvani had noticed that when Royal Society in London in 1800. publications on electricity, he touched a (dead) frog’s leg with Voltaic cells only supply current for he was appointed to teach two dissimilar metals, or applied a short time before the chemical in Como in 1774. The following an electrical spark to it, the leg reactions stop. Later developments year, he developed the twitched. He presumed that the such as the Daniell cell and the electrophorus (an instrument source of this motion was the frog’s modern dry zinc-carbon or alkaline for generating electric charge), body and deduced it contained an cell have greatly improved longevity. and in 1776 he discovered electrical fluid. Volta performed Like alkaline cells, voltaic cells methane. Volta became similar experiments, but without cannot be recharged once professor of physics at Pavia animals, eventually coming up with exhausted, and are termed primary in 1779. There he engaged in the theory that the dissimilarity cells. Secondary cells, like those friendly rivalry with Luigi of the metals in the circuit was found in the lithium polymer Galvani in Bologna. Volta’s the source of the electricity. batteries of cell phones, can be doubts about Galvani’s ideas recharged by applying a potential of “animal electricity” led to Volta’s simple electrochemical difference across the electrodes to his invention of the voltaic cell consists of two metal pieces reverse the chemical reaction. ■ pile. Honored by both (electrodes), separated by a salt Napoleon and the emperor of solution (an electrolyte). Where Austria, Volta was a wealthy each metal meets the electrolyte man in his later years, and a chemical reaction takes place, died in 1827. creating “charge carriers” called ions (atoms that have gained or lost electrons, and so are negatively or positively charged). Oppositely charged ions appear at the two electrodes. Because unlike charges attract each other, separating positive and negative charges requires energy (just as holding The voltaic pile consists of a series of Key work metal disks separated by brine-soaked cloth. A chemical reaction between 1769 On the Forces of them creates a potential difference, Attraction of Electric Fire which drives an electric current.

130 IN CONTEXT EEALNTEEACRXTGROYINCAL KEY FIGURE Georg Simon Ohm ELECTRIC CURRENT AND RESISTANCE (1789–1854) BEFORE 1775 Henry Cavendish anticipates a relationship between potential difference and current. 1800 Alessandro Volta invents the first source of continuous current, the voltaic pile. AFTER 1840 British physicist James Joule studies how resistance converts electrical energy into heat. 1845 Gustav Kirchhoff, a German physicist, proposes rules that govern current and potential difference in circuits. 1911 Dutch physicist Heike Kamerlingh Onnes discovers superconductivity. A s early as 1600, scientists had distinguished “electric” substances, such as amber and glass, from “nonelectric” substances, such as metals, on the basis that only the former could hold a charge. In 1729, British astronomer Stephen Gray brought a new perspective to this division of substances by recognizing that electricity (then, still thought to be a kind of fluid) could travel from one electric substance to another via a nonelectric substance. By considering whether electricity could flow through a substance rather than whether it could be stored, Gray established

ELECTRICITY AND MAGNETISM 131 See also: Electric charge 124–127 ■ Electric potential 128–129 ■ Making magnets 134–135 ■ The motor effect 136–137 ■ Induction and the generator effect 138–141 ■ Electromagnetic waves 192–195 ■ Subatomic particles 242–243 A voltage (potential difference) applied across wire, and the points must be at the two ends in a conductor will cause a current to flow different electric potentials (having an imbalance in charge between through it. the two points). Current flows Typical conductors offer some resistance to this from higher potential to lower (by scientific convention, from positive flow of current. to negative). If the resistance remains constant, then the current In metals, the charge carriers remains proportional to the applied voltage. are negatively charged, so a current flowing in a metal wire from A to B the modern distinction between different energy levels. In metals, is equivalent to negatively charged conductors and insulators. It was there are relatively few electrons electrons flowing in the opposite Alessandro Volta’s invention of the in the outermost orbitals, and direction (toward the higher, or electrochemical cell (battery) in 1800 these electrons easily become relatively positive potential). Charge that finally gave scientists a source “delocalized,” moving freely and carriers in other materials may be of continuously flowing electric randomly throughout the metal. positive. For example, salt water charge—an electric current—to Gold, silver, and copper are excellent contains positively charged sodium study conductance and resistance. conductors because their atoms ions (among others)—and their have only one outermost electron, movement would be in the same Conducting and insulating which is easily delocalized. direction as the flow of current. As Volta’s invention demonstrated, Electrolytes (solutions such as salt Current is measured in units called an electric current can only flow water) contain charged ions that can amps, short for amperes. A current if it has a conductive material move around fairly easily. In contrast, of 1 amp means about 6 trillion through which to travel. Metals are in insulators, the charge carriers are electrons are moving past a generally very good conductors of localized (bound to particular atoms). particular point every second. electricity; ceramics are generally good insulators; other substances, Flow of charge In a copper wire, delocalized such as a salt solution, water, or The modern description of current electrons move around randomly graphite, fall somewhere between. electricity emerged in the late 19th at more than 1,000 km per second. century, when current was finally Because they are moving in random The carriers of electric charge understood to be a flow of positive directions, the net (average) velocity in metals are electrons, which or negatively charged particles. In is zero, and so there is no net ❯❯ were discovered a century later. order for a current to flow between Electrons in atoms are found in two points, they must be connected The beauty of electricity … orbitals at different distances from by a conductor such as a metal is not that the power the nucleus, corresponding to is mysterious and unexpected … but that it is under law. Michael Faraday

132 ELECTRIC CURRENT AND RESISTANCE Current is of equal electromagnetic wave, which decrease in temperature. Some strength in all parts travels extremely quickly. The materials exhibit zero resistance copper wire acts as a “waveguide,” when cooled below a specific, very of the circuit. and electromagnetic energy travels low temperature—a property known Georg Ohm along the wire at (typically) 80–90 as superconductivity. percent of what would be its speed current. Applying a potential in a vacuum—hence electrons The resistance of a conductor difference across the ends of the throughout the circuit all begin to may vary with the potential wire creates an electric field. This drift almost instantaneously, and difference (also known as the field causes the free, delocalized a current is established. voltage) applied or the current electrons to experience a net force flowing through it. For example, the toward the end at high potential Electrical resistance resistance of a tungsten filament (because they are negatively The property of an object to oppose in an incandescent bulb increases charged), accelerating them so that a current is called its resistance. with current. The resistance of they drift through the wire. This drift Resistance (and its opposite, many conductors remains constant velocity constitutes the current, and conductance) depends not only on as the current or voltage varies. it is very small—typically a fraction an object’s intrinsic properties (how Such conductors are known as of a millimeter per second in a wire. the particles that make it up are ohmic conductors, named after arranged, and in particular whether Georg Ohm, who formulated a law Although charge carriers in a the charge carriers are delocalized), that relates voltage to current. wire move relatively slowly, they but also on extrinsic factors such as interact with each other via an its shape, and whether it is subject Ohm’s law electric field (due to their charge) and to high temperature or pressure. The law Ohm established is a magnetic field (created by their A thicker copper wire, for example, that current flowing through movement). This interaction is an is a better conductor than a thinner a conductor is proportional one of the same length. Such factors to the voltage across it. Dividing are comparable with hydraulic the voltage (measured in volts) systems. For example, it is harder to by the current (measured in amps) push water through a narrow pipe gives a constant number, which than through a wide one. is the resistance of the conductor (measured in ohms). Temperature also plays a role in a material’s resistance. The resistance A copper wire is an ohmic of many metals decreases with a conductor—it obeys Ohm’s law as long as its temperature does not Georg Simon Ohm Ohm was born in Erlangen he began to experiment (now Germany) in 1789. His with electricity. At first, his father, a locksmith, taught him publications were not well mathematics and science. He received, partly because of his was admitted to the University of mathematical approach, but also Erlangen and met mathematician because of squabbles over his Karl Christian von Langsdorff. In scientific errors. Later, however, 1806, Ohm’s father, worried that he was awarded the Royal his son was wasting his talents, Society’s Copley Medal in 1841, sent him to Switzerland, where and was made Chair of Physics he taught mathematics and at the University of Munich in continued his own studies. 1852, two years before his death. In 1811, Ohm returned to Key work Erlangen and obtained a doctorate. He moved to Cologne to teach 1827 The Galvanic Circuit in 1817. After hearing of Hans Investigated Mathematically Christian Ørsted’s discoveries,

ELECTRICITY AND MAGNETISM 133 Ohm’s law encapsulates the link between voltage (potential Current Voltage (V) difference), current, and resistance. Its formula (see right) can be (A) = used to calculate how much current (in amps) passes through a component depending on the voltage (V) of the power source Resistance (Ω) and the resistance (measured in ohms) of items in the circuit. Current 5A 5A measured 10V 1A in amps (A) 1V Voltage 1Ω 5V 1Ω 1Ω supplied 1Ω by battery Resistance measured in ohms (Ω) Higher voltage When voltage and increases flow of current resistance are both doubled, as long as resistance Ohm’s law means that stays the same current stays the same change dramatically. The resistance the next in the direction of a the resistance depends on the of ohmic conductors depends on temperature gradient. In describing applied potential difference (or physical factors such as temperature the flow of electrical current, the current flowing). and not on the applied potential potential difference across an difference or the current flowing. electrical conductor is similar to Joule heating the temperature difference across The higher the current in a metal Ohm arrived at his law through two ends of a thermal conductor. conductor, the more collisions a combination of experiments and occur between the electrons and mathematical theory. In some of Ohm’s law is not a universal the ionic lattice. These collisions his experiments, he made circuits law, however, and does not hold result in the kinetic energy of the using electrochemical cells to for all conductors, or under all electrons being converted into supply the voltage and a torsion circumstances. So-called non- heat. The Joule-Lenz law (named in balance to measure current. He ohmic materials include diodes part after James Prescott Joule who used wire of different lengths and the tungsten filament in discovered that heat could be and thicknesses to carry the incandescent bulbs. In such cases, generated by electricity in 1840) electricity and noted the difference states that the amount of heat in current and resistance that generated by a conductor carrying occurred as a result. His theoretical a current is proportional to its work was based on geometrical resistance, multiplied by the methods to analyze electrical square of the current. conductors and circuits. Joule heating (also called ohmic Ohm also compared the flow heating, or resistive heating) has of current with Fourier’s theory of many practical uses. It is responsible heat conduction (named after for the glow of incandescent lamp French mathematician Joseph filaments, for example. However, Fourier). In this theory, heat energy Joule heating can also be a is transferred from one particle to significant problem. In electricity transmission grids, for example, it Filament (incandescent) light bulbs causes major energy losses. These work by providing high resistance to losses are minimized by keeping current electricity because the wire the current in the grid relatively (the filament) is very narrow. This low, but the potential difference resistance causes electrical energy (voltage) relatively high. ■ to be converted to heat and light.

134 EPHOAACWSHAEMRCEETRATLAIN MAKING MAGNETS IN CONTEXT A battery in a A compass needle is complete circuit creates deflected by magnetism. KEY FIGURE Hans Christian Ørsted an electric current. (1777–1851) When an electric current is turned on next to BEFORE a compass needle, the needle moves. 1600 English astronomer William Gilbert realizes that Electricity produces a magnetic field. Earth is a giant magnet. B y the end of the 18th every modern electrical appliance, 1800 Alessandro Volta century, many magnetic from headphones to cars, but it was makes the first battery, and electrical phenomena discovered purely by chance. creating a continuous flow had been noticed by scientists. of electric current for the However, most believed electricity Ørsted’s chance discovery first time. and magnetism to be totally Alessandro Volta’s invention of distinct forces. It is now known the voltaic pile (an early battery) AFTER that flowing electrons produce a in 1800 had already opened up a 1820 André-Marie Ampère magnetic field and that spinning whole new field of scientific study. develops a mathematical magnets cause an electric current For the first time, physicists could theory of electromagnetism. to flow in a complete circuit. This produce a steady electric current. relationship between electricity In 1820, Danish physicist Hans 1821 Michael Faraday creates and magnetism is integral to nearly Christian Ørsted was delivering a the first electric motor and shows electromagnetic rotation in action. 1876 Alexander Graham Bell, a Scottish–American physicist, invents a telephone that uses electromagnets and a permanent horseshoe magnet to transmit sound vibrations.

ELECTRICITY AND MAGNETISM 135 See also: Magnetism 122–123 ■ Electric charge 124–127 ■ Induction and the generator effect 138–141 ■ Force fields and Maxwell’s equations 142–147 lecture to students at the University By passing an electric current Hans Christian Ørsted of Copenhagen. He noticed that a through a wire, Ørsted created compass needle was deflected a magnetic field around it. This Born in Rudkøbing, Denmark, away from magnetic north when he deflected a compass needle. in 1777, Ørsted was mostly switched an electric current on and home-schooled before off. This was the first time a link US’s electrical telegraph network. attending the University of had been shown between an The advantage of an electromagnet Copenhagen in 1793. After electric current and a magnetic is that its magnetic field can be gaining a doctorate in physics field. Ørsted carried out more controlled. Whereas a regular and aesthetics, he was experiments and found that magnet’s strength is constant, the awarded a travel bursary and a current produces a concentric strength of an electromagnet can met German experimenter magnetic field around the wire be varied by changing the current Johann Ritter, who aroused through which it is flowing. flowing through its wire coil (called his interest in the possible a solenoid). However, electromagnets connection between electricity Creating electromagnets only work with a continuous supply and magnetism. Four years after Ørsted’s discovery, of electrical energy. ■ British inventor William Sturgeon In 1806, Ørsted returned to made a magnet from a horseshoe- The agreement of this law Copenhagen to teach. His 1820 shaped piece of iron and wound with nature will be better discovery of the link between it with 18 loops of copper wire. the two forces brought him He passed an electric current seen by the repetition international recognition. He through the wire, magnetizing of experiments than by was awarded the Royal the horseshoe enough for it to Society of London’s Copley attract other pieces of iron. a long explanation. Medal and was later made a Hans Christian Ørsted member of the Royal Swedish In the 1830s, American scientist Academy of Science and the Joseph Henry developed the American Academy of Arts electromagnet further, insulating and Sciences. In 1825, he was copper wire with silk thread and the first chemist to produce winding multiple layers around iron pure aluminum. He died in cores. One of Henry’s magnets lifted Copenhagen in 1851. a weight of 2,064lb (936kg). By the 1850s, small electromagnets were Key works being widely used in receivers in the 1820 “Experiments on the Effect of a Current of Electricity on the Magnetic Needle” 1821 “Observations on Electro-magnetism”

136 IENLEMCOTTRIIOCNITY THE MOTOR EFFECT IN CONTEXT B uilding on Hans Christian currents either attract or repel each Ørsted’s discovery of the other, depending on whether the KEY FIGURE relationship between currents are flowing in the same or André-Marie Ampère electricity and magnetism, French opposite directions. If the current (1775–1836) physicist André-Marie Ampère flows in the same direction in both, conducted his own experiments. then the wires are attracted; if one BEFORE flows in the opposite direction, they 1600 William Gilbert conducts Ørsted had discovered that a repel each other. the first scientific experiments current passing through a wire on electricity and magnetism. forms a magnetic field around the Ampère’s work led to the law wire. Ampère realized that two bearing his name, which states 1820 Hans Christian Ørsted parallel wires carrying electric that the mutual action of two proves that an electric current creates a magnetic field. A magnet creates a A battery produces an magnetic field. electric current, which AFTER 1821 Michael Faraday makes flows through a wire. the first electric motor. When an electric current passes through a 1831 Joseph Henry and magnetic field, it produces a force called Faraday use electromagnetic the motor effect. induction to create the first electric generator, converting The direction of When a loop of wire motion into electricity. the force depends on the carries current in opposite direction of the current. directions, it produces an 1839 Moritz von Jacobi, overall rotational force. a Russian engineer, demonstrates the first practical rotary electrical motor. 1842 Scottish engineer Robert Davidson builds an electric motor to power a locomotive.

ELECTRICITY AND MAGNETISM 137 See also: Electric potential 128–129 ■ Making magnets 134–135 ■ Induction and the generator effect 138–141 ■ Force fields and Maxwell’s equations 142–147 ■ Generating electricity 148–151 lengths of current-carrying wire is rotated 180 degrees, the force The experimental proportional to their lengths and to reverses, so the loop comes investigation by which the magnitudes of their currents. to a halt. Ampère established the law This discovery was the foundation of the mechanical action of a new branch of science known French instrument-maker between electric currents is as electrodynamics. Hippolyte Pixii discovered the one of the most brilliant solution to this conundrum in 1832 advancements in science. Making motors when he attached a metal ring split James Clerk Maxwell When a current-carrying wire is into two halves to the ends of a coil placed in a magnetic field, it with an iron core. This device, a more powerful magnets, increasing is subject to a force because the commutator, reverses the current in the current, or using very thin wire magnetic field interacts with the coil each time it rotates through to increase the number of loops. the field created by the current. half a turn—so the loop continues The closer the magnet to the coil, If the interaction is strong enough, to spin in the same direction. the greater the motor force. the wire moves. The force is at its greatest when the current is In the same year, British Direct-current (DC) motors are flowing at right angles to the scientist William Sturgeon invented still used for small battery-operated magnetic field lines. the first commutator electric motor devices; universal motors, which capable of turning machinery. Five use electromagnets instead of If a loop of wire, with two years later, American engineer permanent magnets, are used for parallel sides, is placed between Thomas Davenport invented a many household appliances. ■ the poles of a horseshoe magnet, the powerful motor that rotated at interaction of the current on one 600 revolutions per minute and side causes a downward force, was capable of driving a printing while there is an upward force on press and machine tools. the other side. This makes the loop rotate. In other words, An electrodynamic world electrical potential energy is Over the years, electrodynamic converted to kinetic (motion) technology produced more powerful energy, which can do work. and efficient motors. Torques However, once the loop has (turning forces creating rotational motion) were increased by using André-Marie Ampère Born to wealthy parents in Lyon, speculated about the existence France, in 1775, André-Marie of “electrodynamic molecules,” Ampère was encouraged to anticipating the discovery of educate himself at home, in a electrons. In recognition of his house with a well-stocked library. work, the standard unit of Despite a lack of formal education, electric current—the amp—is he took up a teaching position at named after him. He died in the new École Polytechnique in Marseilles in 1836. Paris in 1804 and was appointed as professor of mathematics there Key works five years later. 1827 Memoirs on the After hearing of Ørsted’s Mathematical Theory of discovery of electromagnetism, Electrodynamics Phenomena, Ampère concentrated his Uniquely Deduced from intellectual energies into Experience establishing electrodynamism as a new branch of physics. He also

138 IN CONTEXT FOTOHFREMCDAEOGSMNEINTIIOCN KEY FIGURE Michael Faraday (1791–1867) INDUCTION AND THE GENERATOR EFFECT BEFORE 1820 Hans Christian Ørsted discovers the link between electricity and magnetism. 1821 Michael Faraday invents a device that uses the interaction of electricity and magnetism to produce mechanical motion. 1825 William Sturgeon, a British instrument-maker, builds the first electromagnet. AFTER 1865 James Clerk Maxwell presents a paper describing electromagnetic waves, including light waves. 1882 The first power stations to use electricity generators are commissioned in London and New York. E lectromagnetic induction is the production of electromotive force (emf, or a potential difference) across an electrical conductor as the result of a changing magnetic field. Its discovery would transform the world. It is still the foundation of the electricity power industry today, and it made possible the invention of electric generators and transformers, which are at the heart of modern technology. In 1821, inspired by Hans Christian Ørsted’s discovery of the relationship between electricity and magnetism the previous year, British physicist Michael Faraday built two devices that took

ELECTRICITY AND MAGNETISM 139 See also: Electric potential 128–129 ■ The motor effect 136–137 ■ Force fields and Maxwell’s equations 142–147 ■ Generating electricity 148–151 A magnet When a magnet is moved creates a magnetic through a coil of wire, an field around it, and this electric current is induced. is stronger at each pole. When the magnet changes direction, the electric Michael Faraday current changes direction. The son of a London The combination of a magnetic field and continuing blacksmith, Michael Faraday mechanical motion in close proximity causes received a very limited formal a constant electric current. education. However, when he was 20, he heard renowned advantage of the so-called motor mutual induction, and the chemist Humphry Davy effect (the creation of a force when apparatus—an induction ring— lecturing at London’s Royal current passes through a conductor was the world’s first transformer Institution and sent him his in a magnetic field). These devices (a device that transfers electrical notes. Faraday was invited to converted mechanical energy into energy between two conductors). become Davy’s assistant and electrical energy. traveled around Europe with Faraday also moved a magnet him from 1813 to 1815. Faraday conducted many through a coil of wire, making experiments to investigate the electric current flow in the coil as Famous for inventing the interplay of electric currents, he did so. However, once the motion electric motor in 1821, Faraday magnets, and mechanical motion. of the magnet was stopped, the ❯❯ also devised an early form of These culminated in a series Bunsen burner, discovered of experiments from July to benzene, and formulated the November 1831 that would have laws of electrolysis. A pioneer a revolutionary impact. in environmental science, he warned about the dangers of The induction ring I am busy just now pollution in the Thames River. One of Faraday’s first experiments again on electro-magnetism A man of strong principles, he in 1831 was to build an apparatus scorned the pseudoscientific with two coils of insulated wire and think I have got cults of the day. He gave wrapped around an iron ring. When hold of a good thing. Christmas lectures for the a current was passed through one Michael Faraday public, refused to offer advice coil, a current was seen to flow to the government on military temporarily in the other, showing matters, and turned down a up on a galvanometer, a device that knighthood. He died in 1867. had only recently been invented. This effect became known as Key works 1832 Experimental Researches in Electricity 1859 A Course of Six Lectures on the Various Forces of Matter

140 INDUCTION AND THE GENERATOR EFFECT galvanometer registered no to be induced. This could come First finger points in Thumb current: the magnet’s field only about as a result of a change in the the direction of the shows the enabled current to flow when the strength of the magnetic field, or magnetic field direction field was increasing or decreasing. by moving the magnet and the coil of force When the magnet was moved in closer or further from each other, applied the opposite direction, a current or by rotating the coil or turning to the wire was again seen to flow in the coil, the magnet. this time in the opposite direction. Middle finger Faraday also found that a current An American scientist called shows the direction flowed if the coil was moved over Joseph Henry had also discovered of the current a stationary magnet. electromagnetic induction in 1831, independently of Faraday, but The right-hand rule shows the The law of induction Faraday published first and his direction in which a current will Like other physicists of the day, findings became known as flow in a wire when the wire moves Faraday did not understand the Faraday’s law of induction. It in a magnetic field. true nature of electricity—that remains the principle behind current is a flow of electrons—but generators, transformers, and Later, in the 1880s, British physicist he nevertheless realized that when many other devices. John Ambrose Fleming described a a current flows in one coil, it simple way of working out the produces a magnetic field. If the In 1834, Estonian physicist direction of induced current flow: current remains steady, so does Emil Lenz developed the principle the “right-hand rule.” This uses the the magnetic field, and no potential further, stating that the potential thumb, index finger, and middle difference (consequently, no difference induced in a conductor finger of the right hand (held current) is induced in the second by a changing magnetic field perpendicular to one another) to coil. However, if the current in the opposes the change in that magnetic indicate the direction of the current first coil changes, the resulting field. The current resulting from the flow from an induced potential change in magnetic field will induce potential difference generates a difference when a wire moves in a a potential difference in the other magnetic field that will strengthen magnetic field (see diagram, above). coil, so a current will flow. the original magnetic field if its strength is reducing, and weaken it Faraday’s dynamo Faraday’s conclusion was that if its strength is increasing. This In 1831, the same year as Faraday’s no matter how a change in the principle is known as Lenz’s law. experiments on the induction ring, magnetic environment of a coil is One effect of Lenz’s law is that some he also created the first electric produced, it will cause a current electric current is lost and converted dynamo. This was a copper disk to heat. mounted on brass axes that rotated freely between the two poles of a Coil of Magnetic Magnet moves permanent magnet. He connected conducting wire lines of force out of the wire the disk to a galvanometer and found that when it rotated, the Magnet galvanometer registered a current, moves into which moved out from the center the wire of the disk and flowed through a spring contact into a wire circuit. Flow of Galvanometer The apparatus came to be known current measures current as a Faraday disk. When a bar magnet moves in and out of a coil of wire, it The experiment showed that produces an electric current. The direction of current changes the combination of a magnetic according to the direction moved by the magnet. The current field and continuing mechanical produced would be greater with more coils or a stronger magnet.

ELECTRICITY AND MAGNETISM 141 motion in close proximity caused current it produced, however, Now we find all matter subject a constant electric current. In a reversed every half-turn and no one to the dominion of Magnetic motor, the flow of electrons through had yet discovered a practical way of forces, as they before were a wire in a magnetic field induces a harnessing this alternating current known to be to Gravitation, force on the electrons and therefore (AC) electricity to power electronic on the wire, causing it to move. devices. Pixii’s solution was to use Electricity, cohesion. However, in Faraday’s disk (and a device called a commutator to Michael Faraday other generators), the law of convert the alternating current induction applies—a current to a single-direction current. It the springboard for further scientific is produced as a result of the was not until the early 1880s that discovery. In 1861, Scottish physicist motion of a conductor (the disk) the first large AC generators were James Clerk Maxwell simplified in a magnetic field. While the constructed by British electrical the knowledge to date about characteristic of the motor effect is engineer James Gordon. electricity and magnetism to that electrical energy is changed to 20 equations. Four years later, in a mechanical energy, in the generator The first industrial dynamo was paper presented to the Royal Society effect, mechanical energy is built in 1844 in Birmingham, UK, in London (“A dynamical theory of converted to electrical energy. and was used for electroplating. In the electromagnetic field”), Maxwell 1858, a Kent lighthouse became the unified electric and magnetic fields Practical uses first installation to be powered by a into one concept—electromagnetic Faraday’s discoveries required steam-powered electrical generator. radiation, which moved in waves painstaking experimentation but With the coupling of dynamos to at close to the speed of light. produced very practical results. steam-driven turbines, commercial The paper paved the way for the They provided the understanding electricity production became discovery of radio waves and of how to produce electricity on a possible. The first practical for Einstein’s theories of relativity. ■ previously undreamed-of scale. electricity generators went into production in 1870, and by the Although the basic design of the 1880s areas of New York and Faraday disk was inefficient, it would London were lit by electricity soon be taken up by others and produced in this way. developed into practical electricity generators. Within months, French A scientific springboard instrument-maker Hippolyte Pixii Faraday’s work on the relationship had built a hand-cranked generator between mechanical movement, based on Faraday’s design. The magnetism, and electricity was also I have at last Wireless charging inside the device takes power succeeded in from the field and converts it illuminating a Many small battery-operated back into electric current. In magnetic curve … appliances—such as cell small domestic appliances, the and in magnetizing phones, electric toothbrushes, coils are small, so they must be a ray of light. and pacemakers—now use in close contact to work. Michael Faraday induction chargers, which eliminate exposed electrics and Inductive charging is also reduce reliance on plugs and possible for electric vehicles as an cables. Two induction coils in alternative to plug-in charging. close proximity form an In this case, larger coils can be electrical transformer, which used. Robotic, automatic guided charges up an appliance’s vehicles, for example, don’t need battery. The induction coil in to be in contact with the charger a charging base produces an unit, but can simply pull up alternating electromagnetic close by and charge. field, while the receiver coil

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144 FORCE FIELDS AND MAXWELL’S EQUATIONS IN CONTEXT Four equations describe how electric fields, magnetic fields, electric charges, and currents are related. KEY FIGURE James Clerk Maxwell A single equation derived from these four describes the (1831–1879) motion of an electromagnetic wave. BEFORE This electromagnetic wave travels at a constant, very high 1820 Hans Christian Ørsted speed, very close to the observed speed of light. discovers that a current carrying wire deflects the Electromagnetic waves and light needle of a magnetic compass. are the same phenomenon. 1825 André-Marie Ampère lays the foundations for the T he 19th century witnessed was both fundamental and true, the study of electromagnetism. a series of breakthroughs, complexity of the equations (and 1831 Michael Faraday both experimental and perhaps, its revolutionary nature) discovers electromagnetic deductive, that would enable the meant that few other physicists induction. greatest advance in physics since understood it immediately. Isaac Newton’s laws of motion AFTER and gravitation: the theory of In 1873, Maxwell condensed 1892 Dutch physicist Hendrik electromagnetism. The chief the 20 equations into just four, and Lorentz investigates how architect of this theory was in 1885, British mathematician Maxwell’s equations work Scottish physicist James Clerk Oliver Heaviside developed a much for different observers, leading Maxwell, who formulated a set of more accessible presentation that to Einstein’s theory of special equations based upon the work of, allowed a wider community of relativity. among others, Carl Gauss, Michael scientists to appreciate their 1899 Heinrich Hertz discovers Faraday, and André-Marie Ampère. significance. Even today, Maxwell’s radio waves while he is equations remain valid and useful investigating Maxwell’s theory Maxwell’s genius was to place at all but the very smallest scales, of electromagnetism. the work of his predecessors on a where quantum effects necessitate rigorous mathematical footing, their modification. I do not perceive in recognize symmetries among any part of space, the equations, and deduce their Lines of force whether … vacant or filled greater significance in light of In a series of experiments in 1831, with matter, anything but experimental results. Michael Faraday discovered the forces and the lines phenomenon of electromagnetic in which they are exerted. Originally published as 20 induction—the generation of an Michael Faraday equations in 1861, Maxwell’s theory electric field by a varying magnetic of electromagnetism describes field. Faraday intuitively proposed precisely how electricity and a model for induction that turned magnetism are intertwined and out to be remarkably close to our how this relationship generates current theoretical understanding, wave motion. Although the theory

ELECTRICITY AND MAGNETISM 145 See also: Magnetism 122–123 ■ Electric charge 124–127 ■ Making magnets 134–135 ■ The motor effect 136–137 ■ Magnetic monopoles 159 ■ Electromagnetic waves 192–195 ■ The speed of light 275 ■ Special relativity 276–279 although his inability to express Positive Negative coordinates and associated with the model mathematically meant charge Field line charge a number—the temperature that it was ignored by many of his at that point. peers. Ironically, when Maxwell Electric field lines show the direction translated Faraday’s intuition into of the field between charges. The lines Force fields equations, he was in turn initially come together at the negative charge, Taken together, magnetic “field” ignored, because of the forbidding travel away (diverge) from the positive or “flux” lines describe the region depth of his mathematics. charge, and can never cross. around a magnet in which magnetizable bodies “feel” a Faraday was keenly aware attended Faraday’s lectures in force. In this magnetic field, the of a long-standing problem in London, turned the descriptive magnitude of the force at any point physics—namely, how a force could “lines of force” into the mathematical in space is related to the density of be instantaneously transmitted formalism of a field. Any quantity field lines. Unlike a temperature field, through “empty” space between that varies with position can be the points on a magnetic field also separated bodies. There is nothing represented as a field. For example, have a direction, given by the in our everyday experience that the temperature in a room can direction of the field line. A magnetic suggests a mechanism for this be considered a field, with each field is therefore a vector field—each “action at a distance.” Inspired by point in space defined by three spatial point in it has an associated the patterns in iron filings around strength and direction, like the magnets, Faraday proposed that velocity field of flowing water. magnetic effects were carried by invisible lines of force that permeate Similarly, in an electric field, the the space around a magnet. These field line indicates the direction of lines of force point in the direction the force felt by a positive charge, that a force acts and the density of and the concentration of field lines lines corresponds to the strength indicates the strength of the field. of the force. Like typical fluid flows,electric and magnetic fields may change over Faraday’s experimental results time (due, for example, to changing were first interpreted mathematically weather patterns), so the vector at by British physicist J.J. Thomson each point is time-dependent. ❯❯ in 1845, but in 1862 Maxwell, who James Clerk Maxwell Born in Edinburgh in 1831, James Cavendish Laboratory. He made Clerk Maxwell was a precocious enormous contributions to the child and presented a paper on study of electromagnetism, mathematical curves aged just thermodynamics, the kinetic 14. He studied at Edinburgh and theory of gases, and the theory Cambridge universities. In 1856, of optics and color. All of this he was appointed professor at he accomplished in a short life, Marischal College, Aberdeen, before dying of cancer in 1879. where he correctly reasoned that the rings of Saturn were made up Key works of many small solid particles. 1861 On Physical Lines of Force Maxwell’s most productive 1864 A Dynamical Theory of years were at King’s College the Electromagnetic Field London from 1860 and then 1870 Theory of Heat Cambridge from 1871, where he 1873 A Treatise on Electricity was made the first Professor of and Magnetism Experimental Physics at the new

146 FORCE FIELDS AND MAXWELL’S EQUATIONS Maxwell’s first two equations for negative charge. Gauss’s law for The special theory of are statements of Gauss’s laws magnetic fields states that the relativity owes its for electric and magnetic fields. divergence of a magnetic field is zero Gauss’s laws are an application everywhere; unlike electric fields, origins to Maxwell’s of Gauss’s theorem (also known there can be no isolated points from equations of the as the divergence theorem), which which magnetic field lines flow out was first formulated by Joseph-Louis or in. In other words, magnetic electromagnetic field. Lagrange in 1762 and rediscovered monopoles do not exist and every Albert Einstein by Gauss in 1813. In its most magnet has both a north and a south general form, it is a statement pole. As a consequence, magnetic equation relates the rate of change about vector fields—such as fluid field lines always occur as closed flows—through surfaces. loops, so the line leaving a magnet’s of the magnetic field B with time, north pole returns to the south pole Gauss formulated the law for and continues through the magnet to the “curl” of the electric field. The electric fields around 1835, but did to close the loop. curl describes how electric field not publish it in his lifetime. It relates lines circulate around a point. the “divergence” of an electric field The Faraday and Unlike the electric fields created at a single point to the presence Ampère–Maxwell laws by static point charges, which of a static electric charge. The The third of Maxwell’s equations is have divergence but no curl, divergence is zero if there is no a rigorous statement of Faraday’s electric fields that are induced by charge at that point, positive (field law of induction, which the latter changing magnetic fields have lines flow away) for positive charge, had deduced in 1831. Maxwell’s a circulating character, but no and negative (field lines converge) divergence, and can cause current to flow in a coil. Maxwell’s equations The fourth of Maxwell’s E BMaxwell’s four equations contain the variables and , representing equations is a modified version of André-Marie Ampère’s circuital law, the electric and magnetic field strengths, which vary with position and which was originally formulated in time. They may be written as this set of four coupled partial differential 1826. This states that a constant equations. They are “differential” because they involve differentiation, a electric current flowing through a mathematical operation concerned with how things change. They are “partial” conductor will create a circulating because the quantities involved depend on several variables, but each term magnetic field around the conductor. of the equation only considers a part of the variation, such as dependence on time. They are “coupled” because they involve the same variables and Driven by a sense of symmetry, are all simultaneously true. Maxwell reasoned that just as a changing magnetic field generates Name Equation an electric field (Faraday’s law), so a changing electric field should Gauss’s law for electric fields   E  0 generate a magnetic field. In order Gauss’s law for magnetic fields B0 to accommodate this hypothesis,   E  Bt Faraday’s law he added the ∂E/∂t term (which Ampère–Maxwell law   B  0J00 (Et) represents the variation of an electric J  Electric current density (current flowing t  Partial derivate with field, E, in time, t) to Ampère’s law in a given direction through unit area) respect to time to make what is now called the Ampère–Maxwell law. Maxwell’s B E Magnetic field  Electric field   Electric charge density addition to the law was not based   Differential 0  Electric constant (charge per unit volume) operator 0  Magnetic constant

ELECTRICITY AND MAGNETISM 147 on any experimental results but was vindicated by later experiments and advances in theory. The most dramatic consequence of Maxwell’s addition to Ampère’s law was that it suggested that electric and magnetic fields were commonly associated with a wave. Electromagnetic waves established that electromagnetic Heinrich Hertz’s experiments at and light phenomena have a wavelike the end of the 19th century proved what In 1845, Faraday observed that a character (having deduced that Maxwell had predicted and confirmed magnetic field altered the plane of disturbances in the electromagnetic the existence of electromagnetic waves, polarization of light (this is known as field propagate as a wave), but that including radio waves. the Faraday effect). The phenomenon the wave speed, determined of polarization had been discovered theoretically through comparison validity of the theory became by Christiaan Huygens back in 1690, with the standard form of a wave obvious in 1899 when German but physicists did not understand equation, was very close to the physicist Heinrich Hertz—who how it worked. Faraday’s discovery experimentally determined value was determined to test the did not directly explain polarization, for the speed of light. validity of Maxwell’s theory of but it did establish a link between electromagnetism—discovered light and electromagnetism—a Since nothing else but light radio waves. relationship that Maxwell would was known to travel at anything put on firm mathematical footing like the speed of light, Maxwell Maxwell’s four equations a few years later. concluded that light and today underlie a vast range of electromagnetism must be two technologies, including radar, From his several equations, aspects of the same phenomenon. cellular radio, microwave ovens, Maxwell produced an equation that and infrared astronomy. Any described wave motion in three- Maxwell’s legacy device that uses electricity or dimensional space. This was his Maxwell’s discovery encouraged magnets fundamentally depends on electromagnetic wave equation. scientists such as American them. Classical electromagnetism’s The speed of the wave described physicist Albert Michelson to impact cannot be overstated—not by the equation is given by the term seek a more accurate measurement only does Maxwell’s theory contain 1/√(0e0). Maxwell had not only of the speed of light in the 1880s. the fundamentals of Einstein’s Yet Maxwell’s theory predicts an special theory of relativity, it is It turns out that the magnetic entire spectrum of waves, of which also, as the first example of a and the electric force … visible light is only the most easily “field theory,” the model for many is what ultimately is the sensed by humans. The power and subsequent theories in physics. ■ deeper thing … where we can start with to explain many other things. Richard Feynman

148 IN CONTEXT IMOTMHFAPENTRHPIWSOEOIWSLNLUERN KEY FIGURE Thomas Edison (1847–1931) GENERATING ELECTRICITY BEFORE 1831 Michael Faraday shows that a changing magnetic field interacts with an electric circuit to produce an electromagnetic force. 1832 Hippolyte Pixii develops a prototype DC generator based on Faraday’s principles. 1878 German electrical engineer Sigmund Schuckert builds a small steam-driven power station to light a Bavarian palace. AFTER 1884 Engineer Charles Parsons invents the compound steam turbine, for more efficient power generation. 1954 The first nuclear power station goes online in Russia. O n January 12, 1882, the Edison Electric Light Station at Holborn Viaduct in London began to generate electricity for the first time. This facility, the brainchild of prolific American inventor Thomas Edison, was the world’s first coal- fired power station to produce electricity for public use. A few months later, Edison opened a bigger version, at Pearl Street in New York City. The ability to make electricity on a large scale was to be one of the key drivers for the Second Industrial Revolution of 1870–1914. Until the 1830s, the only way of making electricity was by chemical reactions inside a battery. In 1800,