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Gauss and the Global Magnetic Field

Public interest in science owes a great deal to Alexander Von Humboldt (1769--1859). As a young man Alexander explored the jungles of South America, but much of his life was spent in Paris, where he tirelessly drew the public's attention to the achievements of the natural sciences. Late in life he assembled his scientific knowledge into a monumental set of volumes titled Kosmos.

In a 1828 meeting Humboldt suggested to the greatest German mathematician of his time, Carl Friedrich Gauss, that he ought to apply his talents to the mysteries of magnetism. Gauss and his associate Weber then built a laboratory to study magnetism, in which, among other things, they devised the world's first magnetic telegraph.

Up to that time, the compass needle and the downward pointing dip needle on a horizontal axis measured well the direction of the magnetic force, but what about measuring its strength? Gauss devised a clever method for doing so, using an auxiliary magnet; today this is a popular undergraduate lab exercise.

He also knew a method used in celestial mechanics for analyzing gravity, and applied it to the description the Earth's region of magnetic forces, its magnetic field. That method, too, is still in use: it represents the field as the sum of a dominant north-south dipole (2-pole, like a bar magnet) whose strength decreases with distance r like 1/r3, plus a     4-pole decreasing like 1/r4, plus an 8-pole decreasing like 1/r5, and so forth. The field of an isolated monopole would presumable decrease like 1/r2, the way gravity does but no such single pole was ever observed, they always come (at the very least) in pairs.

The new tools for better observation and description of the Earth's magnetic field led to better, world-wide observations. Gauss and Weber organized a Magnetic Union for setting up observatories, and Humboldt enlisted Russia's Czar to create a chain of them across Siberia. The greatest help however came from the British empire, whose Magnetic Crusade led by Sir Edward Sabine set up stations from Canada to Tasmania (then known as Van Diemen's Land). The vast network not only made possible the first global models of the field, but also demonstrated the world-wide character of magnetic storms.

One can compare today's magnetic models, some of them based on satellite observations, to the ones started by Gauss more than 150 years ago. One trend then stands out: the dominant dipole field is getting weaker, at about 5% per century (the rate might have increased since 1970). In the unlikely event that the trend continues unchanged, about 1500-2000 years from now the magnetic polarity of the Earth would reverse.

The magnetic field of the Earth would not disappear, because other field components (4-pole, etc.) are meanwhile growing stronger, and as the late Ned Benton has shown, the total magnetic energy remains practically unchanged. But the dominant compass direction would reverse and fossil magnetism of rocks suggests that this has indeed happened many times in geological history, most recently about 700,000 years ago.

Author and Curator: Dr. David P. Stern


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