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Demagnetization Curve
Permanent magnets operate in that region of the hysteresis loop known as the demagnetization curve. The greater the area under the demagnetization curve the more effective is the material in the permanent magnet. Figure 329 shows a Ushaped magnet with a soft iron bar, sometimes called a keeper, across its open ends. The magnet is provided with an exciting winding that is usually removed after the magnet has been magnetized. It is common practice to use only one turn with a correspondingly heavy current, which is applied for only a fraction of a second. Let N = the number turns in the winding Suppose that for the condition depicted in Fig. 329(a) a current i is applied to the winding such that the magnetizing force is H_{max} in Fig. 330, which shows the curve for the magnetic material. Then H_{max} = NI/l if the reluctance of the horizontal soft iron piece is neglected.
The corresponding flux density throughout the permanent magnet is B_{max} if leakage is neglected. If the current is reduced to zero, the magnetizing force becomes zero and the flux density drops from the value B_{max} to B_{r}, the retentivity. In order to reduce the flux density to zero it is necessary to apply a current in the reverse direction as shown in Fig. 329(b) of such a value as to produce a magnetizing force equal to the coercivity H_{c} in Fig. 330. The portion B_{R}PH_{C} of the curve is known as the demagnetization curve; it represents the region of interest in the operation of permanent magnets.
Suppose that the magnetizing force H_{max} has been applied to the magnet with the current in the direction shown in Fig. 329(a). Then if the current is reduced to zero, without in the meantime reversing its direction, the flux density will not drop to zero but rather to the value B_{r} as mentioned previously and its direction will remain unchanged. If now a current of such a value as to produce a magnetizing force H in Fig. 330 is passed through the winding in the reverse direction as shown in Fig. 329(b), the flux density drops from its value of B_{r} to B. It is important to note that although the direction of the current in Fig. 329(b) is opposite that in Fig. 329(a) the direction of the flux density is the same in both cases. The same magnetic state, i.e., a reduction in the flux density from the value B_{r} to that of B can be produced when there is no current in the winding by introducing an air gap g of the proper length into the magnetic circuit as shown in Fig. 329(c), assuming that leakage can be neglected. This can be shown as follows Let l_{m} = the mean length of the permanent magnet The reluctance of the soft iron pieces on both sides of the air gap is neglected. The mmf for the air gap is
and the mmf for the permanent magnet is
The total mmf F_{t} around the closed flux path must be the sum of these two mmfs, i.e.
Since for the condition represented by Fig. 329(c) there is no current in the exciting winding, the total mmfFt must be zero in accordance with Eq. 334. Hence
Then from Eqs. 377 and 378 there results
The magnetizing force H for the magnet is obtained in terms of H_{a}, the magnetizing force for the air gap, by comparing Eqs. 375 and 376 with Eq. 379 and is found to be
which can be expressed by
This relationship is represented graphically by the straight line OP in Fig. 330. The values of the magnetizing force H and the flux density B for the permanent magnet are determined by the intersection of the line OP with the demagnetization curve. On the basis of no magnetic leakage the flux must be the same in all parts of the magnetic circuit, i.e., in the permanent magnet, in the soft iron pieces, and in the air gap. The flux is expressed by


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