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Aurora Borealis, the Northern Lights, photographed near Fairbanks, Alaska. Such beautiful auroral displays are a common sight in far northern or southern latitudes, but they are quite rare in the middle latitudes. What causes these shimmering curtains of light, and why are they usually visible only near the Earth’s North and South poles? (George
Lepp /Tony Stone Images)

c h a pt e r

Magnetic Fields

Chapter Outline
29.1 The Magnetic Field 29.2 Magnetic Force Acting on a
Current-Carrying Conductor

29.5 (Optional) Applications Involving
Charged Particles Moving in a Magnetic Field

29.3 Torque on a Current Loop in a
Uniform Magnetic Field

29.6 (Optional) The Hall Effect

29.4 Motion of a Charged Particle in a
Uniform Magnetic Field




any historians of science believe that the compass, which uses a magnetic needle, was used in China as early as the 13th century B.C., its invention being of Arabic or Indian origin. The early Greeks knew about magnetism as early as 800 B.C. They discovered that the stone magnetite (Fe3O4 ) attracts pieces of iron. Legend ascribes the name magnetite to the shepherd Magnes, thenails of whose shoes and the tip of whose staff stuck fast to chunks of magnetite while he pastured his flocks. In 1269 a Frenchman named Pierre de Maricourt mapped out the directions taken by a needle placed at various points on the surface of a spherical natural magnet. He found that the directions formed lines that encircled the sphere and passed through two points diametrically opposite eachother, which he called the poles of the magnet. Subsequent experiments showed that every magnet, regardless of its shape, has two poles, called north and south poles, that exert forces on other magnetic poles just as electric charges exert forces on one another. That is, like poles repel each other, and unlike poles attract each other. The poles received their names because of the way a magnet behavesin the presence of the Earth’s magnetic field. If a bar magnet is suspended from its midpoint and can swing freely in a horizontal plane, it will rotate until its north pole points to the Earth’s geographic North Pole and its south pole points to the Earth’s geographic South Pole.1 (The same idea is used in the construction of a simple compass.) In 1600 William Gilbert (1540 – 1603) extended deMaricourt’s experiments to a variety of materials. Using the fact that a compass needle orients in preferred directions, he suggested that the Earth itself is a large permanent magnet. In 1750 experimenters used a torsion balance to show that magnetic poles exert attractive or repulsive forces on each other and that these forces vary as the inverse square of the distance between interacting poles.Although the force between two magnetic poles is similar to the force between two electric charges, there is an important difference. Electric charges can be isolated (witness the electron and proton), whereas a single magnetic pole has never been isolated. That is, magnetic poles are always found in pairs. All attempts thus far to detect an isolated magnetic pole have been unsuccessful. No matterhow many times a permanent magnet is cut in two, each piece always has a north and a south pole. (There is some theoretical basis for speculating that magnetic monopoles — isolated north or south poles — may exist in nature, and attempts to detect them currently make up an active experimental field of investigation.) The relationship between magnetism and electricity was discovered in 1819 when,during a lecture demonstration, the Danish scientist Hans Christian Oersted found that an electric current in a wire deflected a nearby compass needle.2 Shortly thereafter, André Ampère (1775 – 1836) formulated quantitative laws for calculating the magnetic force exerted by one current-carrying electrical conductor on another. He also suggested that on the atomic level, electric current loops are...
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