Magnetic Leakage

Figure 3-18(a) shows a laminated steel core with an air gap of length g. If there were no magnetic leakage the magnetic flux in all parts of the iron in the air gap would have the same value. The broken line in Fig. 3-18 indicates the mean path of the flux when there is no leakage. The leakage may be kept low by placing the exciting winding on the leg of the core that contains the air gap as shown in Fig. 3-18(b) and by keeping the flux density at a low enough value so that the iron does not saturate.

Figure 3-18. (a) Ferromagnetic core with air gap; (b) exciting winding surrounding leg with air gap; (c) exciting winding on leg not containing air gap; (d) fringing at air gap. Note: The effect of fringing is not shown in (a), (b), and (c).

However, if the exciting winding is placed on a leg of the core that does not contain the air gap as shown in Fig. 3-18(c) for example, then appreciable leakage flux will result. In Fig. 3-18(b) the mmf required to maintain the flux along the path from a to a' in a clockwise direction is small and if the core had infinite permeability this mmf would be zero. As a result there would be no mmf to drive flux across the window in the core. If on the other hand the exciting winding is placed on the leg of the core opposite the leg containing the air gap as shown in Fig. 3-18(c), the mmf required to maintain the flux along the path from b to br would be substantial because it would need to be sufficient to overcome the reluctance of the air gap, a condition that would exist even if the iron had infinite permeability. This mmf acts upon the air spaces that parallel the air gap and produces flux in these parallel air spaces, as for example the window in the core of Fig. 3-18(c). Although the electromagnets of Figs. 3-18(b) and 3-18(c) are identical the magnetic leakage in Fig. 3-18(b) is negligible, whereas that in Fig. 3-18(c) is appreciable even if the exciting ampere turns in both cases are the same.

There are arrangements, however, in which it is not possible to have the exciting winding cover the air gap. Here the magnetic leakage may be appreciable. Appreciable leakage fluxes may also be present in magnetic structures with and without air gaps when the iron is saturated magnetically. In precise magnetic calculations of such structures the effect of leakage must be taken into account. Such calculations are seldom straightforward and they are therefore not within the scope of this textbook.