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Hysteresis loop

Magnetic flux density versus magnetic field strength

At the previous chapter we have been talking about the processes taking place inside ferromagnetic materials while being exposed to an external magnetic field. By now we will have a close look at the graph. The magnetic field strength will be noted in Ampere per meter at the x-axis and the magnetic flux density at the y-axis in Tesla. The field strength is related to the external magnetic field and the flux density describes the magnetization of the material. Both variables have already been described at the chapter magnetism.

1.) Initial magnetization curve

At the previous chapter we have seen, that the magnetization of a ferromagnetic material depends on it's "previous history". A nonmagnetic nail can be permanently magnetized by a magnet. Even in the absence of the magnet, the nail remains magnetized. We will observe a non magnetized ferromagnetic material by now. While exposing the nonmagnetic ferromagnetic material to an external magnetic field, we get an initial magnetization curve.

Initial magnetization curve
Figure 1:
Initial magnetization curve of a ferromagnetic material:
At the beginning of our trial there is no external magnetic field and the material is not magnetized, meaning there is no measurable magnetic field outside the material. Now we will start exposing the material to a weak, homogeneous magnetic field which strength will be increased slowly. Even at low field strength, the spins (=microscopic magnets) start tilting into the direction of the external field, meaning the flux density increases incremental. It doesn't increase to the infinite, but the curve starts flattening at the point H1. There is just a limited number of microscopic magnets (atoms) and some of them are harder to tilt than others. Thats basically because the angle between the axis of some grids (grains) and the field lines of the external field differs. The Java-app has shown, that primarily antiparallel magnets are harder to tilt than magnets being perpendicular to the external field. The higher the field strength becomes, the more of those "hard to tilt magnets" start pointing in parallel to the external field, too. As soon as all of the microscopic magnets point into the direction of the external field, the point of magnetic saturation (HS) is reached.

2.) Reducing the magnetic field to zero


Reducing the magnetic field to zero
Figure 2:
The field strength of the external magnetic field is reduced slowly to zero now. Some of the spins start setting at an angle to the external field as soon as it is reduced again. That happens basically to those magnets, whose grid is placed in a great angle according to the external field. As seen at the previous chapter, some of the magnets (depending on the used material) stay in a parallel position (or a small angle) to the original magnetic field. The ferromagnetic material remains partly magnetized after the external field is turned off. This magnetization left behind is called remanence (BR).

3.) Creating an antipodal magnetic field


Creating an antipodal magnetic field
Figure 3:
By now we will expose the ferromagnetic material to an external magnetic field whose field lines are rotated by an angle of 180 degrees compared to the previous field. The place of the magnetic north pole was once the magnetic south pole and vice versa. We are moving to the left at the x-axis of the plot.
Once more the spins start turning into the direction of the external magnetic field. The starting point is not equivalent to the point of origin, because the material is still magnetized caused by the primarily magnetic field. At a certain field strength of the new (antipodal) field, the flux density and so the magnetization becomes zero. At this point the spins of the ferromagnetic material are arranged in a way that there is no magnetization left outside. The field strength needed to degauss the material is called coercive field or coercivity (-HC). At this point the plot cuts the x-axis.
If the field strength of the antipodal field is increased, meaning we are moving to the left of the x-axis, the point is reached where all spins point into the direction of the external magnetic field. The magnetic saturation is reached again, but all magnets are tilted at an angle of 180 degrees. That's demonstrated by the algebraic sign (-HS).

4.) Reducing the antipodal field to zero


Reducing the antipodal field to zero
Figure 4:
Now the antipodal field is reduced to zero. As soon as we do so, some of the magnets start setting an angle to the external field, meaning the flux density is reduced, too. Once again, those spins (atoms) are affected, whose grid is placed in a great angle according to the external field. After turning off the antipodal field, the same magnets will remain in their position who did so after turning off the primarily field. The difference is the fact, that they are tilted at an angle of 180 degrees, too! As a result, the remaining magnetization has the same absolute value like before, just with a minus in front. What was once the magnetic north pole of the material is the magnetic south pole by now and vice versa.

5.) Increasing the primarily magnetic field


Increasing the primarily magnetic field
Figure 5:
Let's increase the field strength once more, pointing in the original direction. Now the processes of the initial magnetization curve take place once again. The difference lies in the fact that we don't start at the point of origin, because the material is still magnetized in height of the remanence (-BR) of the antipodal field. The point of degaussing is reached when the curve cuts the x-axis once again at the point HC. The coercive field strength is needed to degauss the ferromagnetic material.
The values for the point of magnetic saturation are identical to those of the first time we exposed the material to a magnetic field. Analogous we get the same curve as described at 2.) as soon as we reduce the field to zero once more.


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