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8. Gauss and Humboldt
The work of Oersted and Ampére drew to the study of magnetism one of the sharpest minds of Europe, that of Carl Friedrich Gauss (1777-1855). Gauss was a professor of mathematics at the German university of Göttingen and rarely traveled away from home, but in 1828 he attended a conference in Berlin, and stayed there as house guest of Alexander von Humboldt [Dunnington, 1955]. Humboldt (1769-1859) was a naturalist who had earlier explored the jungles of South America and later the author of "Kosmos," a 5-volume encyclopaedic compendium of the natural sciences, which greatly helped spread public interest in science. Humboldt was also quite interested in magnetism [Malin and Barraclough, 1991]. . During this visit he showed Gauss his collection of magnetic instruments and encouraged him to apply his talents to magnetism. That Gauss did, together with his young assistant Wilhelm Weber (1804-91), contributing greatly to the understanding of the Earth's magnetic field [Garland, 1979]. In their magnetism lab, Gauss and Weber constructed the first magnetic telegraph, using it until lightning knocked down the wire. They devised a new suspension for observatory magnets--big magnets, slow to respond, later replaced by more nimble instruments. In 1832 Gauss and Weber also devised a clever method of using an auxiliary magnet to measure not only the direction of the Earth's magnetic force, but also its intensity. Today undergraduate physics students use the Gauss method for measuring the strength of the Earth's field as a standard lab experiment, not realizing its historical significance. Actually it made possible for the first time a global network of magnetic observatories, because now every instrument could be calibrated locally, independently of any others. But perhaps the most lasting contribution was the use of a precise mathematical method to represent the global magnetic field of the Earth and to combine observations at many locations. That was spherical harmonic analysis, previously used for analyzing gravitational fields in celestial mechanics. According to Sidney Chapman, it was introduced to geomagnetism by the French mathematician Simeon Denis Poisson (1781-1840) [Chapman, 1964, p. 4]. The attraction of the Earth's gravity, like that of a single magnetic pole, diminishes with distance R like 1/R22. The force is three-dimensional, but because of its simple structure, a single mathematical expression, known as the harmonic potential, can describe it all. If the Earth repelled instead of attracted, the only change would be a sign reversal. As long as all magnetic forces could be ascribed to a collection of magnetic poles, combinations of such harmonic potentials could describe them as accurately as was desired (this holds in any simply-connected current-free region). With two equal and opposite magnetic poles, one attracts like 1/R2 and the other repels like 1/R2. Far away the distances from the poles are about equal, and the attraction of one tends to cancel the repulsion of the other; but a small difference remains, depending on direction and going down like 1/R3: that is the "dipole" field, the main component of the magnetic field of the Earth, and also of a bar magnet. Combining two equal but slightly separated dipoles that almost cancel each other gives a "4-pole," whose field weakens with distance like 1/R4, and so on: with enough terms, such a "spherical harmonic analysis" can describe the magnetic field to any desired accuracy. Incidentally, to fully describe the field two distinct expansions are needed--one (the main one, in inverse powers of R) for fields originating inside the Earth and another (with positive powers) for those originating on the outside. The method used by Gauss also showed that at least 99% of the field originated inside the Earth. The process somewhat resembles the turning of a square piece of wood into a round wheel. First, cut off the four corners. This leaves 8 obtuse corners, and by cutting off these in a suitable way, one is left with 16 corners, each making an angle only slightly smaller than 180°. Continue the process long enough and your wheel gets as round as you may wish. Today's models of the Earth's magnetic field, derived largely from satellite data, carry those expansions to hundreds of terms [e.g. Olsen et al., 2000]. 9. Explorations and Surveys It took the ingenuity of Gauss and Weber to devise the tools for conducting a global survey of the magnetic field of the Earth. It took crafty politics and the collaboration of many individuals to establish the world-wide network of observatories which actually conducted such a survey. Gauss and Weber started it in 1834 by setting up the "Göttingen Magnetic Union" (Göttingen Magnetischer Verein), an international network of observatories. However, while these observatories covered Europe quite well, most of the world was left uncovered. Alexander Von Humboldt then stepped in and asked for the support of the British Royal Society [Cawood, 1979]. The participation of the British Empire was essential, because it alone had outposts around the globe, and its involvement was helped by the curious fact that due to a kinship of ruling families, Göttingen too was under British rule until 1837. Humboldt also got the Russian Czar to support a chain of observatories across Siberia and even one in Sitka, Alaska, which operated from 1842 to 1864. Humboldt had earlier noted large scale magnetic disturbances (possibly already observed by George Graham) and gave them the name they still bear--"magnetic storms." The world-wide net of magnetic observatories confirmed that such "storms" were world-wide phenomena. The change in the magnetic attraction of the Earth was quite small, rarely exceeding 1% of the total value--but its pattern across the world was remarkably similar, suggesting a large-scale phenomenon. The British participation was greatly helped by three dedicated explorers--Rear Admiral John Ross (1777-1856), his nephew James Clark Ross (1800-62), and an artillery officer named Edward Sabine (1788-1883). For many years the British navy had searched for a "Northwest Passage" to the Pacific Ocean, an east-west sea lane among the icy islands of northern Canada, but all its efforts were blocked by polar ice. The Rosses, with Sabine conducting magnetic observations, tried to get through in 1818 and failed. An 1819 expedition, under Parry, reached a bit further before ice stopped it--but Sabine had sailed with it, and his observations convinced him he had actually passed north of the magnetic pole. The Rosses were denied any further support by the British admiralty, but in 1829 they found an independent backer--Felix Booth, owner of Booth's distillery (Booth's gin is still being made). They bought a 150-ton paddle steamer, the "Victory," and with favorable weather sailed it to the eastern shore of a long peninsula jutting northwards from North America. They named it in honor of their sponsor "Boothia Felix," or "happy land of Booth," which became "Boothia peninsula" on today's maps [Serson, 1981; Barraclough and Malin, 1981]. At Boothia the "Victory" stuck in ice for the winter. In the following summer it managed to move only a few miles, and after the third winter the explorers abandoned it, moved on by sledge and were fortunate to be picked up by a whaling ship. They had not managed to traverse the Northwest Passage. They did however discover the north magnetic pole [Good, 1991]. After a series of careful magnetic measurements, James Clark Ross became convinced that the pole was no more than 100 miles west of the spot where the "Victory" was wedged. In the summer of 1831, aided by local Eskimos (as desolate as the area was, it was inhabited) he set out towards that spot. On June 1 his measurements indicated that he was very close: a horizontal magnetic needle, suspended on a silk string, showed no preference for any direction, and the dip needle pointed within 1 minute of arc of the vertical. Ross spent the entire day making measurements, built a stone cairn to mark the spot, raised the British flag and claimed the land for the British crown. He was lucky to find the magnetic pole so far south: because of the gradual change in the Earth's magnetic field, the pole changes its position, and in 1831 it was near the end of a long southward excursion [Dawson and Newitt, 1982, Figure 1]. It is now at the edge of the Arctic Ocean, far north of where it was then. The south magnetic pole, in Antarctica, was reached by Douglas Mawson in 1909; more recently it has moved off-shore.
When Gauss and Weber began organizing a global magnetic survey, the Rosses and Sabine (later Sir Edward Sabine) became their leading lobbyists and supporters, and soon were the de-facto leaders of a "magnetic crusade." By 1841 much of the world-wide network was actually in operation. The British had set up stations in Greenwich, Dublin, Toronto, St. Helena, Cape of Good Hope and "Van Diemen's Land" (Tasmania), the East India Company (also British) added 4 more in India and Singapore, Russia established 10 stations in its own territory and one in Beijing, while other observatories were set up elsewhere, for a total of 53. The first world-wide survey had begun, a flood of magnetic data began arriving, and the first world-wide magnetic charts could be drawn. The new tool of spherical harmonic analysis provided the first quantitative description of the Earth's magnetic field, both its direction and strength. Since then, magnetic surveys have been carried out repeatedly [Good 1985, 1988, 1994] across land, aboard special non-magnetic ships and most recently by satellites whose orbits sweep above the entire Earth every day. These included surveys by Vanguard 3 in 1959 [Heppner, 1963], by Magsat in 1980 [Langel et al., 1985] and by a Danish satellite aptly named "Oersted", launched in 1999 [Olsen et al., 2000] , as well as by some Soviet satellites. Many scholars--most recently, Jeremy Bloxham [1992; Bloxham and Gubbins, 1989] and Andrew Jackson--also collected earlier compass observations and tried to derive from them models of the field before the era of Gauss, as well as of its slow "secular" variation. The analysis has shown, as expected, that the 2-pole ("dipole") part of the field greatly exceeded all others. In other words, the 2-pole terrella has always been a good approximation to the actual field, although--if one wants to be a stickler for accuracy--the magnetic center, the location of the dipole which fits observations best, is offset a few hundred kilometers from the Earth's center. The surprising feature is that since the time of Gauss, the strength of this "dipole" component has steadily declined by about 5% per century, the decline accelerating somewhat after 1970. Even though the measured strength of the magnetic field is decreasing, it would be more accurate to say that it is becoming more complex, rather than weaker. As the dipole part of the field is weakening, the more complex parts (4-pole etc.) are gaining strength. In other words--as the strength of the field associated with the largest spatial scale (dipole) decreases, that associated with smaller scales increases. If all the Earth's magnetism comes from its liquid core (whose radius, about half the Earth's, is known from seismology), the non-dipole components of the field are much stronger there, because they diminish much faster with distance R, like higher powers of R. Theory suggests that the total magnetic energy cannot easily change as quickly as the observed changes in the field. Calculations indeed confirm that the sum-total of that energy has changed very little--just that the complicated parts have grown at the expense of the dipole, and since those decrease faster with distance, the field at the surface has weakened too. So--if we wait 1500-2000 years, is it possible that the dipole part will become very small, while the overall structure of the field becomes complex, with perhaps more than one pair of magnetic poles? And could it be that 2000 years after that, the dipole part will have continued to grow in the opposite direction, until it again dominated the global structure of the magnetic field, the way it does now--but with opposite polarity? The geomagnetic record suggests this is not likely to happen, and that the trend will probably change. However, it also tells us (as discussed in a later section) that the above scenario cannot be ruled out, and that such reversals have apparently happened many times during the Earth's magnetic past. 10. Faraday's Lines of Force (field lines) Gauss avoided speculating on the source of the Earth's magnetism. Just measuring it accurately was challenging enough--and in the process, proving that it originated inside the Earth, not outside it. The first steps towards understanding that source were made by a slightly younger contemporary, Michael Faraday [Williams, 1965; Segré, 1984]. Faraday (1791-1867) was the son of an English blacksmith, apprenticed by his parents to a bookbinder. Faraday took advantage of his job to read books brought to the bindery, among them a volume of the Encyclopaedia Britannica with an article about electricity. Science aroused his interest and as a young man he attended free scientific lecturers by Humphry Davy, Britain's leading chemist [Knight, 2000], taking careful notes of what he heard. When Davy dismissed his assistant for brawling and advertised for a replacement, Faraday applied, sending his notes as proof of his interest--and ended up with the job. Starting as little more than Davy's servant, Faraday rose to make a name for himself in the study of chemistry and magnetism, discovering (for instance) the basic laws of electrolysis. What he lacked in formal schooling and mathematical analysis he made up in intuition and insight. He had a remarkable talent of expressing complicated scientific ideas in simple words, and was noted for his lucid lectures and writings. One notable contribution was a simple way of visualizing the magnetic force. When Gilbert explored the "orb of virtue" around his terrella, the region where magnetic forces could be sensed, he found that at every point in space, the force on his magnetic needle (including the downward dip) had a certain direction. Faraday made visible the overall pattern of those directions, by connecting them with continuous lines.
Those "lines of force" (today we call them field lines) spread out from the south pole of the terrella, arch around its middle and converge again near the north pole (Figure 6). This not only describes the pattern of the directions of the magnetic force. It also tells about the strength of that force: where the lines crowd together, the force is strong, where they are spaced widely apart it is weak. [Please note: Purists sometimes name the ends of a bar magnet "north seeking" and "south seeking" rather than "north" and "south", because if the Earth's field were due to a bar magnet near its center, the north-seeking end of that bar would be closer to the south magnetic pole, and vice versa.] Magnetic field lines have a strange history. They started out as no more than a visualization aid, like lines of latitude and longitude, which have no real existence but merely help visualize positions on the globe. Faraday, however felt [Baggott, 1991] that space in which magnetic forces could exist was itself modified, and such space later became known as a "magnetic field." Faraday's younger contemporary, James Clerk Maxwell--a good friend and outstanding physicist, but unlike Faraday, also a skilled mathematician--extended that notion and showed that an "electromagnetic field" could support a wave motion which spread at the velocity of light and had the observed properties of light. Light, radio waves, x-rays, microwaves--all belong to the same family, making the concept of electromagnetic fields one of the foundations of modern science and engineering. More was to come in the 20th century. Much of space above the Earth's atmosphere (and indeed, throughout the universe) contains plasmas--gases hot enough to contain free electrons and positive "ions," atoms stripped of some electrons. The Sun consists of plasma, space around Earth is filled with plasma, and in such plasmas, only very occasionally do free electrons re-combine with positive ions, usually not for long. This is quite unlike the familiar environment near the surface of the Earth, where free ions and electrons are rare and neutral atoms and molecules are the rule. In most of space, plasmas are so rarefied that collisions are rare, and ions and electrons spiral around magnetic field lines, guided by them the way a bead is guided by a wire on which it is strung [e.g. Cowling, 1957, or any text on plasma physics]. Magnetic field lines in space thus assume yet another role--defining the direction in which ions and electrons travel most easily, as do electric currents and heat carried by them. Plasma waves also flow differently along magnetic field lines and across them. In a rarefied plasma, magnetic field lines are like the grain in a piece of wood, which outlines the "easy" direction in which the wood readily splits. All these concepts sprang from the visual and intuitive imagination of Faraday, from a simple idea which grew into an extremely useful and versatile one. 11. Faraday's Disk Dynamo Oersted and Ampére had shown that electric currents were the primary source of magnetism--e.g. a current following a wire, wrapped around an iron core, turned it into a magnet. However, reversing the process--winding a conducting wire around a magnet--did not produce any electric current. Instead, Faraday discovered that electric currents were generated in a closed conducting circuit only if that circuit sensed a changing magnetic field. The change could come from variations in the strength of the magnetic source, or it could arise from relative motion between the source and the conductor. This led to machines--once called "dynamos," though today "generators" is the more common term--in which conductors are whirled around and around, through the fields of magnets, producing electric currents. To serve a useful purpose (e.g. charge a storage battery), those currents of course had to be led outside the rotating part. That is usually done by metal rings attached to the rotating shafts (but electrically insulated from them), connected to the rotating wires while at the same time touching sliding contacts mounted on the non-rotating part. From the sliding contacts other wires lead the current to wherever it is needed. Not every motion qualifies, because there is also the matter of energy. As Ampére had shown, a wire carrying an electric current through the magnetic field encounters a force. Only when the force opposes the motion, so that one has to invest energy to overcome it, does a current flow--and not surprisingly, the energy invested exactly equals the energy needed to drive the current. Like a careful accountant, nature always balances her ledger books.
Using these principles, Faraday devised the simplest of all dynamos, the so-called "Faraday disk." Imagine the space between the poles of a magnet (Figure 7), with straight magnetic field lines connecting one pole to the other. In that space a metal disk rotates on a shaft parallel to the field lines. The shaft and disk form the moving part of the circuit: the magnet and the wires that complete the circuit are stationary, and the wires are electrically linked to the disk by two sliding contacts, one on the axle, one near the periphery. Because of the symmetric arrangement of the disk and magnetic field, the current also tends to flow symmetrically (a symmetry upset by the placement of the sliding contacts and external circuit)--from the axle to the rim, or vice versa, depending on the direction of rotation and on the magnetic polarities of the two magnet faces. Suppose it flows from the axle to the rim: the magnetic force on an electric current is perpendicular to both the current and the magnetic field lines, so with appropriate rotation of the disk, it resists the rotation. By overcoming that resistance, we invest energy, which re-appears as the energy needed to drive the electric current, creating a dynamo. (Inject current from some outside battery, rotate in the opposite direction so that the motion is helped by the magnetic force rather than opposed by it, and you gain energy. Instead of a dynamo, you have a motor. Many types of dynamos can similarly become motors rotating in the opposite direction. In some electric cars, the motor becomes a dynamo when the car coasts downhill, braking its motion and at the same time returning energy to the storage battery.) While Faraday's disk dynamo illustrates the principle of dynamo action, it is not a practical generator of electricity, unless one requires huge currents driven by tiny voltages. To carry such currents, very massive conductors would be needed, and the copper wiring used in conventional machinery would be completely inadequate. But in a large volume filled with conducting material--for instance, the liquid core of the Earth, believed to be largely molten iron, or on the Sun--such flows are quite possible, and one notes that instead of a solid wheel, a rotating fluid eddy would serve just as well. That idea ultimately became the foundation of modern dynamo theory, briefly described in section 14, which seeks to explain how the magnetic fields of the Sun and the planets--including Earth--are generated.
Faraday had also experimented with electric currents flowing through glass containers from which most air had been removed. In those rarefied gases he observed glows somewhat similar to the polar aurora or "northern lights." He therefore speculated that the Gulf Stream, a broad flow in the Atlantic Ocean along the US Eastern seaboard, may similarly generate a voltage, and if its circuit was closed through the high atmosphere, it might generate there the light of the polar aurora. His speculation was completely wrong, since the actual atmosphere is too poor a conductor of electricity to complete the circuit between the ocean to the upper atmosphere; but otherwise the mechanism was in principle possible.
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