21.1

Magnetic Fields

Permanent magnets have long been used in navigational compasses. As Figure 21-1 illustrates, the compass needle is a permanent magnet supported so it can rotate freely in a plane. When the compass is placed on a horizontal surface, the needle rotates until one end points approximately to the north. The end of the needle that points north is labeled the north magnetic pole; the opposite end is the south magnetic pole.

Figure 21-1 The needle of a compass is a permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.

Magnets can exert forces on each other. Figure 21-2 shows that the magnetic forces between north and south poles have the property that

> like poles repel each other, and unlike poles attract.

This behavior is similar to that of like and unlike electric charges. However, there is a significant difference between magnetic poles and electric charges. It is possible to separate positive from negative electric charges and produce isolated charges of either kind. In contrast, no one has found a magnetic monopole (an isolated north or south pole). Any attempt to separate north and south poles by cutting a bar magnet in half fails, because each piece becomes a smaller magnet with its own north and south poles.

Figure 21-2 Bar magnets have a north magnetic pole at one end and a south magnetic pole at the other end. (a) Like poles repel each other, and (b) unlike poles attract.

Surrounding a magnet, there is a magnetic field. The magnetic field is analogous to the electric field that exists in the space around electric charges. Like the electric field, the magnetic field has both a magnitude and a direction. We postpone a discussion of the magnitude until Section 21.2, concentrating our attention here on the direction. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. In Figure 21-3 the compass needle is symbolized by an arrow, the head of the arrow being the north pole. The drawing shows how compasses can be used to map out the magnetic field in the space around a bar magnet. Since like poles repel and unlike poles attract, the needle of each compass becomes aligned relative to the magnet in the manner shown in the picture. The compass needles provide a visual picture of the magnetic field that the bar magnet creates.

Figure 21-3 At any location in the vicinity of a magnet, the north pole (the arrowhead in this drawing) of a small compass needle points in the direction of the magnetic field at that location.

To help visualize the electric field, we introduced electric field lines in Section 18.7. In a similar fashion, it is possible to draw magnetic field lines, and Figure 21-4a illustrates some of the lines around a bar magnet. The lines appear to originate from the north pole and end on the south pole; they do not start or stop in midspace. A visual image of the magnetic field lines can be created by sprinkling finely ground iron filings on a piece of paper that covers the magnet. Iron filings in a magnetic field behave like tiny compasses and align themselves along the field lines, as the photo in Figure 21-4b shows.

Figure 21-4 (a) The magnetic field lines and (b) the pattern of iron filings (dark, curved regions) in the vicinity of a bar magnet. (© Yoav Levy/Phototake) (c) The magnetic field lines in the gap of a horseshoe magnet.

As is the case with electric field lines, the magnetic field at any point is tangent to the magnetic field line at that point. Furthermore, the strength of the field is proportional to the number of lines per unit area that passes through a surface oriented perpendicular to the lines. Thus, the magnetic field is stronger in regions where the field lines are relatively close together and weaker where they are relatively far apart. For instance, in Figure 21-4a the lines are closest together near the north and south poles, reflecting the fact that the strength of the field is greatest in these regions. Away from the poles, the magnetic field becomes weaker. Notice in part c of the drawing that the field lines in the gap between the poles of the horseshoe magnet are nearly parallel and equally spaced, indicating that the magnetic field there is approximately constant.
Although the north pole of a compass needle points northward, it does not point exactly at the north geographic pole. The north geographic pole is that point where the earth’s axis of rotation crosses the surface in the northern hemisphere (see Figure 21-5). Measurements of the magnetic field surrounding the earth show that the earth behaves magnetically almost as if it were a bar magnet.* As the drawing illustrates, the orientation of this fictitious bar magnet defines a magnetic axis for the earth. The location where the magnetic axis crosses the surface in the northern hemisphere is known as the north magnetic pole. The north magnetic pole is so named because it is the location toward which the north end of a compass needle points. Since unlike poles attract, the south pole of the earth’s fictitious bar magnet lies beneath the north magnetic pole, as Figure 21-5 indicates.

Figure 21-5 The earth behaves magnetically almost as if a bar magnet were located near its center. The axis of this fictitious bar magnet does not coincide with the earth’s rotational axis; the two axes are currently about 11.5° apart.

The north magnetic pole does not coincide with the north geographic pole but, instead, lies at a latitude of nearly 80°, just northwest of Ellef Ringnes Island in extreme northern Canada. It is interesting to note that the position of the north magnetic pole is not fixed, but moves over the years. Pointing as it does at the north magnetic pole, a compass needle deviates from the north geographic pole. The angle that a compass needle deviates is called the angle of declination. For New York City, the present angle of declination is about 12° west, meaning that a compass needle points 12° west of geographic north.
Figure 21-5 shows that the earth’s magnetic field lines are not parallel to the surface at all points. For instance, near the north magnetic pole the field lines are almost perpendicular to the surface of the earth. The angle that the magnetic field makes with respect to the surface at any point is known as the angle of dip.
The physics of navigation in animals. Some animals can sense the earth’s magnetic field and use it for navigational purposes. Until recently (2004), the only examples of this ability were in vertebrates, or animals that have a backbone, such as migratory birds. Now, however, researchers have found that the spiny lobster (see Figure 21-6), which is an invertebrate, can also use the earth’s magnetic field to navigate and can determine its geographic location in a way similar to that of a person using the Global Positioning System (see Section 5.5). This ability may be related to the presence in the lobsters of the mineral magnetite, a magnetic material used for compass needles.

Figure 21-6 Spiny lobsters use the earth’s magnetic field to navigate and determine their geographic position. (Courtesy Kenneth Lohmann, University of North Carolina at Chapel Hill)

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.