A Brief History of The Development of Classical Electrodynamics, Lecture notes of Electromagnetism and Electromagnetic Fields Theory

Download A Brief History of The Development of Classical Electrodynamics and more Lecture notes Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity! 1 A Brief History of The Development of Classical Electrodynamics Professor Steven Errede UIUC Physics 435, Fall Semester 2007 Loomis Laboratory of Physics The University of Illinois @ Urbana-Champaign 900 BC: Magnus, a Greek shepherd, walks across a field of black stones which pull the iron nails out of his sandals and the iron tip from his shepherd's staff (authenticity not guaranteed). This region becomes known as Magnesia. 600 BC: Thales of Miletos (Greece) discovered that by rubbing an 'elektron' (a hard, fossilized resin that today is known as amber) against a fur cloth, it would attract particles of straw and feathers. This strange effect remained a mystery for over 2000 years. 1269 AD: Petrus Peregrinus of Picardy, Italy, discovers that natural spherical magnets (lodestones) align needles with lines of longitude pointing between two pole positions on the stone. ca. 1600: Dr. William Gilbert (court physician to Queen Elizabeth) discovers that the earth is a giant magnet just like one of the stones of Peregrinus, explaining how compasses work. He also investigates static electricity and invents an electric fluid which is liberated by rubbing, and is credited with the first recorded use of the word 'Electric' in a report on the theory of magnetism. Gilbert's experiments subsequently led to a number of investigations by many pioneers in the development of electricity technology over the next 350 years. ca. 1620: Niccolo Cabeo discovers that electricity can be repulsive as well as attractive. 1630: Vincenzo Cascariolo, a Bolognese shoemaker, discovers fluorescence. 1638: Rene Descartes theorizes that light is a pressure wave through the second of his three types of matter of which the universe is made. He invents properties of this fluid that make it possible to calculate the reflection and refraction of light. The ``modern'' notion of the aether is born. 1638: Galileo attempts to measure the speed of light by a lantern relay between distant hilltops. He gets a very large answer. 1644: Rene Descartes theorizes that the magnetic poles are on the central axis of a spinning vortex of one of his fluids. This vortex theory remains popular for a long time, enabling Leonhard Euler and two of the Bernoullis to share a prize of the French Academy as late as 1743. 1657: Pierre de Fermat shows that the principle of least time (using variational calculus) is capable of explaining refraction and reflection of light. Fighting with the Cartesians begins. (n.b. This principle for reflected light had been anticipated anciently by Hero of Alexandria.) 1665: Francesco Maria Grimaldi, in a posthumous report, discovers and gives the name of diffraction to the bending of light around opaque bodies. 1667: Robert Hooke reports in his Micrographia the discovery of the rings of light formed by a layer of air between two glass plates. These were actually first observed by Robert Boyle, which explains why they are now called Newton's rings. In the same work he gives the matching-wave-front derivation of reflection and refraction that is still found in most introductory physics texts. These waves travel through the aether. He also develops a theory of color in which white light is a simple disturbance and colors are complex distortions of the basic simple white form. 2 1671: Isaac Newton destroys Hooke's theory of color by experimenting with prisms to show that white light is a mixture of all the colors and that once a pure color is obtained it can never be changed into another color. Newton argues against light being a vibration of the ether, preferring that it be something else that is capable of traveling through the aether. He doesn't insist that this something else consist of particles, but allows that it may be some other kind of emanation or impulse. In Newton's own words, ``...let every man here take his fancy.'' 1675: Olaf Roemer repeats Galileo's experiment using the moons of Jupiter as the distant hilltop. He measures c = 2.3x108 m/s. 1678: Christiaan Huygens introduces his famous construction and principle, thinks about translating his manuscript into Latin, then publishes it in the original French in 1690. He uses his theory to discuss the double refraction of Iceland Spar. His is a theory of pulses, however, not of periodic waves. 1717: Isaac Newton shows that the ``two-ness'' of double refraction clearly rules out light being aether waves. (All aether wave theories were sound-like, so Newton was correct: longitudinal waves cannot be polarized.) 1728: James Bradley shows that the orbital motion of the earth changes the apparent motions of the stars in a way that is consistent with light having a finite speed of travel. 1729: Stephen Gray shows that electricity doesn't have to be made in place by rubbing, but can also be transferred from place to place with conducting wires. He also shows that the charge on electrified objects resides on their surfaces. 1733: Charles Francois du Fay discovers that electricity comes in two kinds, which he called resinous (−) and vitreous (+). 1742: Thomas Le Seur and Francis Jacquier, in a note to the edition of Newton's Principia that they publish, show that the force law between two magnets varies as the inverse cube of their separation. 1745: Pieter van Musschenbroek invents the Leyden jar, or capacitor, and nearly kills his friend Cunaeus. 1747: Benjamin Franklin invents the one-fluid theory of electricity, in which one of Nollet's fluids exists and the other is just the absence of the first. Franklin also proposes the principle of conservation of charge and calls the fluid that exists and flows ``positive''. {This educated guess ensures that undergraduates will always be confused about the direction of current flow.} He also discovers that electricity can act at a distance in situations where fluid flow makes no sense. 1748 : Sir William Watson uses an electrostatic machine and a vacuum pump to make the first glow discharge. His glass vessel is three feet long and three inches in diameter: the first fluorescent light bulb. 1749: Abbe Jean-Antoine Nollet invents the two-fluid theory electricity. 1750: John Michell discovers that the two poles of a magnet are equal in strength and that the force law for individual poles is inverse square. 1752: Johann Sulzer puts lead and silver together in his mouth, performing the first recorded ``tongue test'' of a battery. 5 1817: Augustin Fresnel annoys the French Academy. The Academy, hoping to destroy the wave theory once and for all, proposes diffraction as the prize subject for 1818. To the chagrin of the particle-theory partisans in the Academy, the winning memoir in 1818 is that of Augustin Fresnel, who explains diffraction as the mutual interference of the secondary waves emitted by the unblocked portions of the incident wave, in the style of Huygens. One of the judges from the particle camp of the Academy is Poisson, who points out that if Fresnel's theory were to be indeed correct, then there should be a bright spot at the center of the shadow of a circular disc. This, he suggests to Fresnel, must be tested experimentally. The experiment doesn't go as Poisson hopes, however, and the spot becomes known as ``Poisson's spot.'' 1820: Hans Christian Oersted discovers that electric current in a wire causes a compass needle to orient itself perpendicular to the wire. 1820: Andre Marie Ampere, a French mathematician, one week after hearing of Oersted's discovery, shows that parallel currents attract each other and that opposite currents attract. He was the first to explain the electro-dynamic theory. A permanent memorial to Ampere is the use of his name for the unit of electric current. 1820: Jean-Baptiste Biot and Felix Savart show that the magnetic force exerted on a magnetic pole by a wire falls off like 1/r and is oriented perpendicular to the wire. Whittaker then says that ``This result was soon further analyzed,'' to obtain: 1820: John Herschel shows that quartz samples that rotate the plane of polarization of light in opposite directions have different crystalline forms. This difference is helical in nature. 1821: Michael Faraday begins electrical work by repeating Oersted's experiments. 1821: Humphrey Davy shows that direct current is carried throughout the volume of a conductor and establishes that: for long wires. He also discovers that resistance is increased as the temperature rises. 1822: Thomas Johann Seebeck discovers the thermoelectric effect by showing that a current will flow in a circuit made of dissimilar metals if there is a temperature difference between the metals. 1824: Poisson invents the concept of the magnetic scalar potential and of surface and volume pole densities described by the formulas: He also finds the magnetic field inside a spherical cavity within magnetized material. 1825: Ampere publishes his collected results on magnetism. His expression for the magnetic field produced by a small segment of current is different from that which follows naturally from the Biot-Savart law by an additive term which integrates to zero around closed circuit. It is unfortunate that electrodynamics and relativity decide in favor of Biot and Savart rather than for the much more sophisticated Ampere, whose memoir contains both mathematical analysis and experimentation, artfully blended together. In this memoir are given some special instances of the result we now call Stokes theorem or as we usually write it . Maxwell describes this work as ``one of the most brilliant achievements in science. The whole, theory and 6 experiment, seems as if it had leaped, full-grown and full-armed, from the brain of the `Newton of electricity'. It is perfect in form and unassailable in accuracy; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electrodynamics.'' 1825: Fresnel shows that combinations of waves of opposite circular polarization traveling at different speeds can account for the rotation of the plane of polarization. 1826: Georg Simon Ohm, a German mathematician and physicist, was a college teacher in Cologne. He established the result now known as Ohm's law. V=IR seems a pretty simple law to name after someone, but the importance of Ohm's work does not lie in this simple proportionality. What Ohm did was develop the idea of voltage as the driver of electric current. He reasoned by making an analogy between Fourier's theory of heat flow and electricity. In his scheme temperature and voltage correspond as do heat flow and electrical current. It was not until some years later that Ohm's electroscopic force (V in his law) and Poisson's electrostatic potential were shown to be identical. In 1827 he published, "The Galvanic Circuit Investigated Mathematically". His theories were coldly received by German scientists, however his research was recognized in Britain and he was awarded the Copley Medal in 1841. His name has been given to the unit of electrical resistance. 1827: Augustin Fresnel publishes a decade of research in the wave theory of light. Included in these collected papers are explanations of diffraction effects, polarization effects, double refraction, and Fresnel's sine and tangent laws for reflection at the interface between two transparent media. 1827: Claude Louis Marie Henri Navier publishes the correct equations for vibratory motions in one type of elastic solid. This begins the quest for a detailed mathematical theory of the aether based on the equations of continuum mechanics. 1827: F. Savery, after noticing that the current from a Leyden jar magnetizes needles in alternating layers, conjectures that the electric motion during the discharge consists of a series of oscillations. 1828: George Green generalizes and extends the work of Lagrange, Laplace, and Poisson and attaches the name potential to their scalar function. Green's theorems are given, as well as the divergence theorem (Gauss's law), but Green doesn't know of the work of Lagrange and Gauss and only references Priestly's deduction of the inverse square law from Franklin's experimental work on the charging of hollow vessels. 1828: Augustine Louis Cauchy presents a theory similar to Navier's, but based on a direct study of elastic properties rather than using a molecular hypothesis. These equations are more general than Navier's. In Cauchy's theory, and in much of what follows, the aether is supposed to have the same inertia in each medium, but different elastic properties. 1828: Poisson shows that the equations of Navier and Cauchy have wave solutions of two types: transverse and longitudinal. Mathematical physicists spend the next 50 years trying to invent an elastic aether for which the longitudinal waves are absent. 1831: Michael Faraday reasoned: If electricity could produce magnetism, then why couldn't magnetism produce electricity? Faraday found the solution. Electricity could be produced through magnetism by motion. He discovered that when a magnet was moved inside a coil of copper wire, a tiny electric current flowed through the wire. Of course, by today's standards, Faraday's electric dynamo/electric generator was crude, and provided only a small electric current, 7 however he discovered the first method of generating electricity by means of motion in a magnetic field. Faraday convincingly showed the world that changing currents in one circuit induce currents in a neighboring circuit. Over the next several years he performed hundreds of experiments and showed that his results could all be explained by the idea of changing magnetic flux. No mathematics was involved, just picture-thinking using his concept of magnetic field-lines. Faraday also investigated many other aspects of electromagnetism, the unit of capacitance (Farad) is named in honor of him. 1831: Ostrogradsky rediscovers the divergence theorem of Lagrange, Gauss, and Green. 1832 :Joseph Henry independently discovers induced currents. 1833: Faraday begins work on the relation of electricity to chemistry. In one of his notebooks he concludes after a series of experiments, ``...there is a certain absolute quantity of the electric power associated with each atom of matter.'' 1834: Faraday discovers self inductance. 1834: Jean Charles Peltier discovers the flip side of Seebeck's thermoelectric effect. He finds that current driven in a circuit made of dissimilar metals causes the different metals to be at different temperatures. 1834: Emil Lenz formulates his rule for determining the direction of Faraday's induced currents. In its original form it was a force law rather than an induced emf law: ``Induced currents flow in such a direction as to produce magnetic forces that try to keep the magnetic flux the same.'' So Lenz would predict that if you try to push a conductor into a strong magnetic field, it will be repelled. He would also predict that if you try to pull a conductor out of a strong magnetic field that the magnetic forces on the induced currents will oppose the pull. 1835: James MacCullagh and Franz Neumann extend Cauchy's theory to crystalline media 1837: Faraday discovers the idea of the dielectric constant. 1837: George Green attacks the elastic aether problem from a new angle. Instead of deriving boundary conditions between different media by finding which ones give agreement with the experimental laws of optics, he derives the correct boundary conditions from general dynamical principles. This advance makes the elastic theories not quite fit with light. 1838: Faraday shows that the effects of induced electricity in insulators are analogous to induced magnetism in magnetic materials. Those more mathematically inclined immediately appropriate Poisson's theory of induced magnetism, inventing , , and . 1838: Faraday discovers Faraday's dark space, a dark region in a glow discharge near the negative electrode. 1839: James MacCullagh invents an elastic aether in which there are no longitudinal waves. In this aether the potential energy of deformation depends only on the rotation of the volume elements and not on their compression or general distortion. This theory gives the same wave equation as that satisfied by and in Maxwell's theory. 1839: William Thomson (Lord Kelvin) removes some of the objections to MacCullagh's rotation theory by inventing a mechanical model which satisfies MacCullagh's energy of rotation hypothesis. It has spheres, rigid bars, sliding contacts, and flywheels. 10 1854: Thomson, in a letter to Stokes, gives the equation of telegraphy ignoring the inductance: , where R is the cable resistance and where C is the capacitance per unit length. Since this is the diffusion equation, the signal does not travel at a definite speed. 1855: Faraday retires, living quietly in a house provided by the Queen until his death in 1867. 1855: James Clerk Maxwell writes a memoir in which he attempts to marry Faraday's intuitive field line ideas with Thomson's mathematical analogies. In this memoir the physical importance of the divergence and curl operators for electromagnetism first become evident. The following equations appear in this memoir: 1857: Gustav Kirchoff derives the equation of telegraphy for an aerial coaxial cable where the inductance is important and derives the full telegraphy equation: : , where L and C are the inductance per unit length and the capacitance per unit length. He recognizes that when the resistance is small, this is the wave equation with propagation speed , which for a coaxial cable turns out to be very close to the speed of light. Kirchoff notices the coincidence, and is thus the first to discover that electromagnetic signals can travel at the speed of light. 1861: Bernhard Riemann develops a variant of Weber's electromagnetic theory, which is also wrong. 1861: Maxwell publishes a mechanical model of the electromagnetic field. Magnetic fields correspond to rotating vortices with idle wheels between them and electric fields correspond to elastic displacements, hence displacement currents. The equation for now becomes , where is the total current, conduction plus displacement, and is conserved: . This addition completes Maxwell's equations and it is now easy for him to derive the wave equation exactly as done in our textbooks on electromagnetism and to note that the speed of wave propagation was close to the measured speed of light. Maxwell writes, ``We can scarcely avoid the inference that light in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.'' Thomson, on the other hand, says of the displacement current, ``(it is a) curious and ingenious, but not wholly tenable hypothesis.'' 1864: Maxwell reads a memoir before the Royal Society in which the mechanical model is stripped away and just the equations remain. He also discusses the vector and scalar potentials, using the Coulomb gauge. He attributes physical significance to both of these potentials. He wants to present the predictions of his theory on the subjects of reflection and refraction, but the requirements of his mechanical model keep him from finding the correct boundary conditions, so he never does this calculation. 1867: Stokes performs experiments that kill his own anisotropic inertia theory. 1867: Joseph Boussinesq suggests that instead of aether being different in different media, perhaps the aether is the same everywhere, but it interacts differently with different materials, similar to the modern electromagnetic wave theory. 1867: Riemann proposes a simple electric theory of light in which Poisson's equation is replaced by . 1867: Ludwig Lorenz develops an electromagnetic theory of light in which the scalar and vector potentials, in retarded form, are the starting point. He shows that these retarded potentials each satisfy the 11 wave equation and that Maxwell's equations for the fields and can be derived from his potentials. His vector potential does not obey the Coulomb gauge, however, but another relation now known as the Lorenz gauge. Although he is able to derive Maxwell's equations from his retarded potentials, he does not subscribe to Maxwell's view that light involves electromagnetic waves in the aether. He feels, rather, that the fundamental basis of all luminous vibrations is electric currents, arguing that space has enough matter in it to support the necessary currents. 1868: Maxwell decides that giving physical significance to the scalar and vector potentials is a bad idea and bases his further work on light on and . 1869: Maxwell presents the first calculation in which a dispersive medium is made up of atoms with natural frequencies. This makes possible detailed modeling of dispersion with refractive indices having resonant denominators. 1869: Hittorf finds that cathode rays can cast a shadow. 1870: Helmholtz derives the correct laws of reflection and refraction from Maxwell's equations by using the following boundary conditions: , , and are continuous. Once these boundary conditions are taken, Maxwell's theory is just a repeat of MacCullagh's theory. The details were not given by Helmholtz himself, but appear rather in the inaugural dissertation of H. A. Lorentz. 1870-1900: The hunt is on for physical models of the aether which are natural and from which Maxwell's equations can be derived. The physicists who work on this problem include Maxwell, Thomson, Kirchoff, Bjerknes, Leahy, Fitz Gerald, Helmholtz, and Hicks. ca.1870: Thomas Alva Edison builds the first practical DC (Direct Current) generator, setting the stage for future commercial power generation (and consumption).Edison's many inventions included the phonograph and an improved printing telegraph. In 1878 Joseph Swan, a British scientist, invented the incandescent filament lamp and within twelve months Edison made a similar discovery in America. Swan and Edison later set up a joint company to produce the first practical filament lamp. Prior to this, electric lighting had been my crude arc lamps. Edison used his DC generator to provide electricity to light his laboratory and later to illuminate the first New York street to be lit by electric lamps, in September 1882. Edison's successes were not without controversy, however - although he was convinced of the merits of DC for generating electricity, other scientists in Europe and America recognized that DC brought major disadvantages. George Westinghouse was a famous American inventor and industrialist who purchased and developed Nikola Tesla's patented motor for generating alternating current. The work of Westinghouse, Tesla and others gradually persuaded American society that the future lay with AC rather than DC (The adoption of AC generation enabled the transmission of large amounts of electrical, power using higher voltages via transformers, which would have been impossible otherwise). Today the unit of measurement for magnetic fields commemorates Tesla's name. When Edison's generator was coupled with James Watt's steam engine, large-scale electricity generation became a practical proposition. James Watt, the Scottish inventor of the steam-condensing engine, was born in 1736. His improvements to steam engines were patented over a period of 15 years, starting in 1769 and his name was given to the electric unit of power, the Watt. Watt's steam engines used the reciprocating piston, however, today's thermal power stations use steam turbines, following the Rankine cycle, 12 worked out by another famous Scottish engineer, William J.M Rankine, in 1859. 1872: E. Mascart looks for the motion of the earth through the aether by measuring the rotation of the plane of polarization of light propagated along the axis of a quartz crystal. No motion is found with a sensitivity of . 1873: Maxwell publishes his Treatise on Electricity and Magnetism, which discusses everything known at the time about electromagnetism from the viewpoint of Faraday. His own theory is not very thoroughly discussed, but he does introduce his electromagnetic stress tensor in this work, including the accompanying idea of electromagnetic momentum. 1875: John Kerr shows that ordinary dielectrics subjected to strong electric fields become double refracting, showing directly that electric fields and light are closely related. 1876: Henry Rowland performs an experiment inspired by Helmholtz which shows for the first time that moving electric charge is the same thing as an electric current. 1876: A. Bartoli infers the necessity of light pressure from thermal arguments, thus beginnning the exploration of the connection between electromagnetism and thermodynamics. 1879: J. Stefan discovers the Stefan-Boltzmann law, i.e., that radiant emission is proportional to . 1879: Edwin Hall performs an experiment that had been suggested by Henry Rowland and discovers the Hall effect, including its theoretical description by means of the Hall term in Ohm's law. 1879: Sir William Crookes invents the radiometer and studies the interaction of beams of cathode ray particles in vacuum tubes. 1879: Ludwig Boltzmann uses Hall's result to estimate the speed of charge carriers (assuming that charge carriers are only of one sign.) 1880: Rowland shows that Faraday rotation can be obtained by combining Maxwell's equations and the Hall term in Ohm's law, assuming that displacement currents are affected in the same way as conduction currents. 1881: J. J. Thomson attempts to verify the existence of the displacement current by looking for magnetic effects produced by the changing electric field made by a moving charged sphere. 1881: George Fitz Gerald points out that J. J. Thomson's analysis is incorrect because he left out the effects of the conduction current of the moving sphere. Including both currents makes the separate effect of the displacement current disappear. 1881: Helmholtz, in a lecture in London, points out that the idea of charged particles in atoms can be consistent with Maxwell's and Faraday's ideas, helping to pave the way for our modern picture of particles and fields interacting instead of thinking about everything as a disturbance of the aether, as was popular after Maxwell. 1881: Albert Michelson and Edwin Morley attempt to measure the motion of the earth through the aether by using interferometry. They find no relative velocity. Michelson interprets this result as supporting Stokes hypothesis in which the aether in the neighborhood of the earth moves at the earth's velocity. 1883: Fitz Gerald proposes testing Maxwell's theory by using oscillating currents in what we would now call a magnetic dipole antenna (loop of wire). He performs the analysis and discovers that very high