According to the longitudinal magnetization law of cuboid steel component (magnetic charges will distribute uniformly along all edges of the cuboid ) and the demagnetization law of ferromagnetic materials (the difficult degree of destruction of a magnetic dipole chain depends on the magnitude of its magnetic potential energy), this paper theoretically clarifies the reason, why the magnetic polarity in a slot on the work piece surface after discontinuation of longitudinal magnetization is just opposite to it, when the specimen is being magnetized.
In magnetic particle inspection experiment a queer phenomenon is discovered that the magnetic polarity in a slot on the work piece surface after discontinuation of magnetization is just opposite to it, when the specimen is being magnetized, that is, the magnetic residual field shows negative values (Fig.1). Dr. F. Förster from Germany recorded this most striking fact by experiment (Fig.2), pointing out that this phenomenon happens in the condition, when the applied magnetizing field Ha is from o approximately up to the coercivity JHC of the sample material, and he introduced a hypothesis that there is a detour magnetic flux dipole beneath the root of the slot, so as to explain the cause of this strange phenomenon .
According to magnetic dipole theory, the author gives another simpler and clearer theoretical explanation of this knotty problem in this paper.
a. At magnetization
b. After discontinuation of magentization
|Fig 1: The direction of magentic field in the slot on work piece surface.|
Ha applied magnetization field; Hi magnetic field in the slot
|Fig 2: The experimental result of Dr. F. Förster |
Keywords: Reversing of magnetic polarity, Negative residual value, Magnetic dipole chain,Magnetic dipole theory, Magnetic potential energy.
1. Basic fundamentals
1.1 From the view point of magnetic charge in the electromagnetism, the magnetization of magnetic medium is practically the orientation (arrangement in good order) of the (molecular) magnetic dipoles along the direction of the applied magnetizing field Ha, and the magnetic dipole chains parallel to the applied field are formed in the magnetic medium [2,3].
The author has already proved that after longitudinal magnetization, the magnetic charges will uniformly distribute along all the edges of a cuboid steel component and a square steel component with rectangular slot as shown in Fig.3 [3,4]. This is the logical conclusion of the principle, that in a stable system of magnetic charges, the interactive energy between all magnetic charges must take the minimum value[5,6].
The scheme of the magnetic dipole chains in a square steel component with a rectangular slot after longitudinal magnetization is shown in Fig.4.
The distribution of magnetic charges after longitudinal magnetization
Magnetic dipole chains in a square steel component with a slot after longitudinal magnetization
1.2 At the magnetization of magnetic medium, the (molecular) magnetic dipoles from irregular arrangement change into the orientation of the applied field, the work of the applied magnetizing field W for surmounting the frictional resistance of solid, transforms into the inner energy of the magnetic dipole chains Ein.
After discontinuation of magnetization of the sample (that is, the applied magnetizing field Ha is removed), the (molecular) magnetic dipoles will return to irregular orientation due to the thermal movement of them. But the restoration of the magnetic dipoles is resisted by the frictional force of the solid too, to force them to maintain their magnetization condition. So only those magnetic dipoles, whose inner energy Ein is very large, can return to their initial orientation before magnetization, overcoming the frictional resistance force of solid .
2. Analysis and discussion
From Fig.4 it isn't difficult to see that turning magnetic dipole chains parallel with Ha to start and stop at the edges parallel with Hais easier than turning them to start and stop at the edges perpendicular to Ha, because the change of direction for the former is small, but for the latter, the rotated angle of magnetic dipole chains must be quite large. So the work done by the magnetizing field for the former is smaller than it for the latter. In other words, after longitudinal magnetization the potential energy of the magnetic charges along every edge parallel with Ha is lower than it along each edge perpendicular to Ha. In the same principle, for the edges parallel with Ha, the shorter the length of the edge, the lower the magnetic potential energy of the magnetic charges along it (Because there are only rare magnetic dipoles, whose orientation must be changed).
| Hi magnetic field in the slot|
Magnetic charges along the edges of slot bottom.
Therefore, after discontinuation of longitudinal magnetization (that is, the applied magnetizing field Ha is removed), only along the edges of slot bottom, having smallest magnetic potential energy, there is still possibility maintaining magnetic charges excited in the magnetization, as shown in Fig.5.
Obviously, at this time the magnetic polarity of these magnetic charges is just opposite to that in the slot at magnetization (Fig.1a).
In addition, due to the narrow edges of the slot bottom and the rare magnetic charges remaining along them, so after discontinuation of magnetization, the opposite residual magnetic field strength must be very low as shown by the experimental result (Fig.2),
To sum up, after discontinuation of longitudinal magnetization the reversing of magnetic polarity in the slot on the work piece surface is the inevitable outcome of the fact, that the magnetic charge must uniformly distribute along every edges of a square steel component after longitudinal magnetization , and the negative residual magnetic field strength must be very low -- the magnetic dipole theory easily and satisfactorily explains the theoretical problem of this knotty phenomenon.
The author gratefully acknowledges the advisements and help of Prof. Wei-Yi Zheng, Senior Engineer Liang-Zhong Liu and the financial support of this work by The National Natural Science Foundation of China.
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