phy1020.DVI

because the Earth’s magnetic dipole is not aligned with the geographic axis, but is tilted at some angle. The
magneticSpole is currently located in the Arctic Ocean north of Canada, and the magneticNpole is located
just off the coast of Antarctica. For reasons that are not currently understood, the magnetic poles “wander”
across the Earth’s surface, so the location of the magnetic poles changes from one year to the next.
The strength of the Earth’s magnetic field may be characterized by its dipole moment, which has a value
ofmD7:94 1022 Am^2. It can be shown that the magnetic fieldBof a magnetic dipole at positionrfrom
the dipole is given by

B.r/D

 0

4



mC3.mOr/Or

r^3



: (33.1)

Using this equation, we can find the expected strength of the Earth’s magnetic field at the Earth’s surface by
substitutingrDRE, whereREis the Earth’s radius. Assuming the Earth’s magnetic field to be a perfect
dipole, the magnetic field at the Earth’s equator should be roughly. 0 =.4//.m=RE^3 /,orBD30;000nT.
The magnetic field at the poles should be twice this value, orBD60;000nT. The actual values at the equator
and poles differ somewhat from these values because the Earth’s magnetic field is not a perfect dipole. In
fact, it’s about 90% dipole, and about 10% higher-order components.

33.2 Magnetic Declination

Because the Earth’s magnetic dipole axis is tilted with respect to the geographic axis, a magnetic compass
will generally not point toward true geographic north; it will point towardmagneticnorth. The difference (the
angle between the two norths) is called themagnetic declination. A map showing lines of equal magnetic
declination (Fig. 33.2) is called anisogonic chart.
As you can see from this chart, there is a 0 ıline of magnetic declination (theagonic line) running near
the Mississippi River; along this line, there is no magnetic declination, and a magnetic compass will point
to true north. Maryland is at about 11 ıwest declination, meaning that a magnetic compass points about 11 ı
west of true north. To get the compass needle to point togeographicnorth, you would need to adjust the
compass dial by 11 ı.
Since the magnetic poles are wandering with time, the isogonic lines change from one year to the next. If
you plan on using a magnetic compass for sailing, hiking, orienteering, or similar activities, you should make
sure you have an up-to-date isogonic chart or something similar that shows the current magnetic declination
for your location. Of course, if you’re traveling large distances, your magnetic declination will be changing
as you move, so you will need to re-adjust your compass for declination from time to time.

33.3 Magnetic Inclination

We often think of the Earth’s magnetic field as running north-south, but it also has a largeverticalcomponent:
downward in the northern hemisphere, and upward in the southern hemisphere. This vertical component is
calledmagnetic inclination.
Because of magnetic inclination, a compass needle will be correctly balanced only for use in a certain part
of the world. For example, a magnetic compass made for use in the United States will have a needle that’s
heavier on theSside than theNside, to compensate for the downward component of the Earth’s magnetic
field and allow the needle to balance properly. If you take this compass and try to use it in Australia, the
compass needle will not balance properly.