As noted in the page for demonstration 68.03 – Magnets on swivels, people discovered the phenomenon of magnetism at least as early as about 600 BCE, when Thales of Miletus discovered that lodestone attracted pieces of iron. It took some time for people to realize that the earth as a whole possessed a magnetic field, and that one could use this as the basis for a navigation aid, the magnetic compass. The first clear description of such a device appears in a Chinese work written in around 1080 CE. The first mention of it in a European work dates to around 1190 CE. The magnetic field of the earth resembles that of a large bar magnet set in the center of the earth, not quite parallel to its axis of rotation. That is, the geomagnetic poles are close to the geographic poles (but oppositely oriented; geomagnetic north is a south magnetic pole, and geomagnetic south is a north magnetic pole), but not exactly aligned with them. Relative to the earth’s surface, the field lines enter or exit the earth vertically at the geomagnetic poles. As you go away from the poles, the angle at which the field lines enter or exit the earth decreases, until midway between the poles, the field lines are horizontal. A magnetic compass, whose needle sits in the horizontal plane, responds to the horizontal component of the magnetic field. This component is zero at the (geomagnetic) poles, and maximum at the (geomagnetic) equator. At any point that is not near one of the magnetic poles, the north end of a compass needle points to geomagnetic north. The angle between the orientation of the compass needle and the direction to the geographic north pole, True north, is called the magnetic declination, and it varies according to one’s location on earth.

As noted above, the magnetic field lines enter or exit the earth at an angle that depends on location. If you mount a magnetic needle so that it can rotate in the vertical plane, you can set the pivot so that the needle rotates to be parallel with the field lines that penetrate the earth’s surface at your location. Such a needle is called a dip needle, and it shows the angle at which the magnetic field exits or enters the earth at a particular point. This angle is called the magnetic inclination, magnetic dip, or dip angle. At the magnetic north pole, the inclination is 90°. As you go south from there, the inclination decreases until is it zero at the magnetic equator, and it becomes increasingly negative as you continue toward the magnetic south pole, where it is -90°.

The prevailing theory regarding what gives the earth its magnetic field (and also gives other planets, and stars and galaxies their magnetic fields) is called the dynamo theory, or more specifically, the self-excited dynamo. As noted on the page for demonstration 16.39 – Cavendish balance, the measured average density of the earth is greater than the average density of the crust, which suggests that the core of the earth is significanty denser than the crust. Careful analysis of seismological data supports this observation, and also shows that at the center of the earth is a solid inner core, surrounded by an outer liquid core. The relatively high density of the core suggests that it is rich in nickel and iron. The outer core, then is a rotating, electrically conductive liquid. This rotating liquid is subject to Coriolis forces, and also to convection currents established by the temperature gradient between the inner and outer boundaries of the liquid outer core. These phenomena together produce electrical currents that give the earth its magnetic field.

The name for the theory comes from analogy to the way a dynamo works. In a typical dynamo, a coil or set of coils is wound on an armature, which sits between the poles of a permanent magnet. When you turn the armature, the changing magnetic flux through the coils induces an electromotive force (emf) in them, which causes current to flow. (See, for example, demonstration 72.12 – AC/DC generator.) In a self-excited dynamo, the permanent magnets are replaced by a second set of coils. When you spin the armature, the residual magnetic field in the armature produces a changing flux in the fixed coils, causing current to flow in them. This produces a magnetic field, which in turn induces an emf in the armature coils, causing current to flow in them.

If you have an accurate magnetometer (and for declination, a good reference for geographic north), it is possible to measure the earth’s magnetic field at a particular point. Such measurements can, however, be affected by stray magnetic fields from nearby geological formations, or from buildings or other nearby structures. Scientists use magnetometers in satellites and on the ground to measure the magnetic field at various points on the earth. From these data, they can construct a mathematical model of the earth’s magnetic field. One such model is the World Magnetic Model (WMM), a joint U.S.-British project. Another is the International Geomagnetic Reference Field (IGRF), produced by geomagnetists from around the world. The earth’s magnetic field is not static, but is constantly changing. Scientists use historical data to track changes in the magnetic field, and to determine how quickly it is currently changing. These models are made to account for the rate at which these changes are occurring, and they are updated every five years. If the latest measurements show that the field is changing more quickly than anticipated, the groups that maintain the WMM may issue an out-of-cycle update. You can find information about these and other models at the links below.

The National Centers for Environmental Information of the National Oceanic and Atmospheric Administration hosts a web page called NCEI Geomagnetic Calculators. If you enter “Broida Hall” for the location, the coordinates that appear are 34°24′50″ (34.4139°) N, 119°50′34″ (119.8428°) W. The exact values the model gives for the magnetic data vary slightly according to the date on which you use the model, but should be reasonably close to the values given here. These are:

	WMM-2020	IGRF-2020
Declination	11.93°	11.95°
Inclination	58.84°	58.85°
Horizontal Intensity	0.239 gauss	0.239 gauss
Total Intensity	0.462 gauss	0.462 gauss

References:

1) Mills, Alan A. Annals of Science, 61 (2004), 273-319 (The Lodestone: History, Physics, and Formation).
2) Chaisson, Eric and McMillan, Steve. Astronomy Today (Upper Saddle River, New Jersey: Prentice-Hall, 1999), pp. 153-162.
3) National Centers for Environmental Information (NCEI) of the National Oceanic and Atmospheric Administration (NOAA) geomagnetism page.
4) Earth’s magnetic Field: The Force That’s Always With You.
5) NCEI geomagnetism FAQ page.
6) NCEI World Magnetic Model page.
7) NCEI International Geomagnetic Reference Field page.
8) British Geological Survey Global Geomagnetic Models page.
9) International Association of Geomagnetism and Aeronomy page.
10) Roberts, Paul H. and King, Eric M. Reports on Progress in Physics 76 (2013).