n/A fluxgate compass.may be obsoleted by flash memory in the near future.
The memory property of ferromagnets can be depicted on the
type of graph shown in figure m, known as a hysteresis curve. The
y axis is the magnetization of a sample of the material — a mea-
sure of the extent to which its atomic dipoles are aligned with one
another. If the sample is initially unmagnetized, 1, and a fieldH
is externally applied, the magnetization increases, 2, but eventu-
ally becomes saturated, 3, so that higher fields do not result in any
further magnetization, 4. The external field can then be reduced,
5, and even eliminated completely, but the material will retain its
magnetization. It is a permanent magnet. To eliminate its magneti-
zation completely, a substantial field must be applied in the opposite
direction. If this reversed field is made stronger, then the substance
will eventually become magnetized just as strongly in the opposite
direction. Since the hysteresis curve is nonlinear, and is not a func-
tion (it has more than one value ofMfor a particular value ofB), a
ferromagnetic material does not have a single, well-defined value of
the permeabilityμ; a value like 4,000 for transformer iron represents
some kind of a rough average.
The fluxgate compass example 26
The fluxgate compass is a type of magnetic compass without
moving parts, commonly used on ships and aircraft. An AC cur-
rent is applied in a coil wound around a ferromagnetic core, driv-
ing the core repeatedly around a hysteresis loop. Because the
hysteresis curve is highly nonlinear, the addition of an external
field such as the Earth’s alters the core’s behavior. Suppose, for
example, that the axis of the coil is aligned with the magnetic
north-south. The core will reach saturation more quickly when
the coil’s field is in the same direction as the Earth’s, but will not
saturate as early in the next half-cycle, when the two fields are
in opposite directions. With the use of multiple coils, the com-
ponents of the Earth’s field can be measured along two or three
axes, permitting the compass’s orientation to be determined in
two or (for aircraft) three dimensions.
Sharp magnet poles example 27
Although a ferromagnetic material does not really have a single
value of the magnetic permeability, there is still a strong tendency
to haveB‖ ≈0 just outside the magnet’s surface, for the same
reasons as discussed above for high-permeability substances in
general. For example, if we have a cylindrical bar magnet about
the size and shape of your finger, magnetized lengthwise, then
the field near the ends is nearly perpendicular to the surfaces,
while the field near the sides, although it may be oriented nearly
parallel to the surface, is very weak, so that we still haveB‖ ≈- This is in close analogy to the situation for theelectricfield
near the surface of a conductor in equilibrium, for whichE‖= 0.
Section 11.7 Electromagnetic properties of materials 743