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Ideal Behavior of an Electromagnet
Ideal Behavior of an Electromagnet
An electromagnet, upon being energized by a current, can induce a magnetic moment on a nearby ferromagnetic object and mechanically pull it. Ideally, the mechanical force an electromagnet exerts is expressed as
where
Departures from ideal behavior
Departures from ideal behavior
Leakage Flux
Leakage Flux
The above equations assumes that the interior magnetic flux created by the solenoid is distributed uniformly. This is not the case for realistic magnets for several reasons. The length of the magnet is finite. The flux is more uniform if the magnet is longer and slenderer. The core and the slug are of finite permeability and cannot confine the magnetic field to the air gap. Also, not all magnetic flux lines are directed at the ferromagnetic media. Flux lines that miss the media are called leakage. [4] Figure III.A.1 shows an example of leakage flux in a 2-winding transformer.
Figure III.A.1: Flux that does not go through both sets of windings are called leakage flux. Image from Electrical4u.
Figure III.A.2: Typical Hysteresis Loop for a Ferromagnetic Material.Magnetic flux density is plotted against magnetic field intensity .Note that bringing H to zero will not bring B to zero.
Nonlinear relationship between B and H / Hysteresis
Nonlinear relationship between B and H / Hysteresis
Another major contributor to nonideal behavior is the physical nature of and hysteresis phenomenon found in all ferromagnetic materials. For an ideal magnet, the magnetic field H is is related directly proportionally to both the current flowing through the winding and the magnetic flux B.
However, the permeability μ is not constant but varies heavily in any ferromagnetic material according to the intensity of the magnetic field. Furthermore, the ferromagnetic material is affected by hysteresis. The current will not just produce a magnetic field but also magnetize the ferromagnetic solenoid core, which retains its magnetization after de-energization. The magnetic force that a solenoid exerts is not just due to the current that is currently energizing it but also the current that previously energized it. [4] As shown in Figure III.A.2, bringing the current in the coil down to zero will not totally eliminate the magnetic field generated by the solenoid. To eliminate the magnetic field, a current in the opposite direction must be applied or the ferromagnetic material must be heated.
[4] C. K. J. S. D. U. A.E. Fitgerald, "Chapter 1: Magnetic Circuit and Magnetic Materials; Chapter 2: Transformers," in Electric Machinery, New York, NY, McGraw-Hill, 2003, p. 19~30; 57 ~ 59.
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