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# Hysteresis

Author: E.E. Kimberly

The theory advanced by Weber is probably the best explanation of the magnetic phenomenon known as hysteresis. He supposes that the molecules of all matter are small magnets. The molecules of iron are strong magnets, and those of all other kinds of matter are weak magnets. When a piece of iron is not magnetized, the molecules lie in no orderly position, and the north poles and south poles are in such disorder that no appreciable lines of force leave the mass. However, under the urge of a magnetomotive force, the molecules tend to arrange themselves parallel to the lines of force acting upon them. In soft iron many molecules are thus rearranged against the stresses of their original positions; but, when the magnetizing force is removed, almost all return to their original positions and there is again disorder. The few molecules that retain their new positions produce a faint remanent magnetic field around the iron. In very hard steel, a greater portion of the total number of molecules that are rearranged adopt the new positions permanently; and, when the magnetizing force is removed, they produce a strong permanent magnetic field around the iron. To rearrange a given number of molecules requires a much stronger magnetizing force in hard steel than in soft steel or iron.

If a bar of magnetically inert steel be surrounded by a solenoid, the magnetomotive force produced may be varied at will by varying the current in the solenoid. In Fig. 7-7 (a) is shown a plot of flux 0 in a given circuit of hard steel as a function of magnetizing ampere-turns.

 Fig. 7-7. The Hysteresis Loop

The molecules cannot be rearranged without work being done on them. If the magnetization be carried to b, the relation of ϕ to NI will follow the curve Ob and the work done will be proportional to the area Obe. If now the magnetizing force be removed slowly, the ratio of ϕ to NI will follow the curve bc. The remaining flux cO when NI = 0 is called the remanent flux and is a measure of degree of permanent magnetism. An amount of work proportional to area ebc will be returned to the solenoid circuit by induction, while work proportional to area Obc will have been used in overcoming the molecular friction of the process and will appear as heat in the iron. Upon reversal of current in the solenoid, the magnetizing force may be carried to d and to f. After a second reversal of current, the magnetizing force may be carried to b. For any value, say NI', there may be either of the two values ϕ1 or ϕ2 after the iron has a magnetic history of at least one cycle. The loop bcdfb is called the hysteresis loop1 and its area is a measure of the hysteresis energy per cycle converted into heat.

Iron subjected to the magnetizing force of an alternating current passes through one hysteresis cycle for every cycle of the current. By experiment it has been found that hysteresis loss in iron approximately is proportional to the 1.6 power of the maximum flux density. Fig. 7-7 (b) shows a typical hysteresis loop for soft iron as used in most electrical machinery.

The hysteresis loss per pound is different for different kinds of iron and steel, and is an important item to be included in purchase specifications. Producers of magnetic sheet steel usually provide this information in the form of a curve such as that in Fig. 7-8.

The hysteresis loss is proportional to the frequency and to the volume of iron, but is not affected by lamination, as is the eddy-current loss. The magnetic quality of iron is affected by heattreating and by mechanical working
 Fig. 7-8. Hysteresis Loss in Iron (for one frequency)

 1 Electric and Magnetic Measurements, by C. M. Smith, The Macmillan Co., New York. Home Electromagnets Hysteresis

Last Update: 2010-10-05