In the previous two sections, we assumed that all flux produced by a coil is contained within the core. This is not always the
case, as we have seen in Section 9.4. There are conditions under which some of the flux closes outside the core or there is no
core to begin with. Consider two coils in air. In this case, we do not know how much of the flux connects the two coils, but we
can assume that a fraction of the flux produced by one coil links the second coil. Suppose this fraction is k. Because of that,
the mutual inductances also change by this fraction; that is, if all flux links both coils, the inductances in Eq. (10.47) are
obtained. If only a fraction k links coil 1 and coil 2, we get
In the previous two sections, we assumed that all flux produced by a coil is contained within the core. This is not always thecase, as we have seen in Section 9.4. There are conditions under which some of the flux closes outside the core or there is nocore to begin with. Consider two coils in air. In this case, we do not know how much of the flux connects the two coils, but wecan assume that a fraction of the flux produced by one coil links the second coil. Suppose this fraction is k. Because of that,the mutual inductances also change by this fraction; that is, if all flux links both coils, the inductances in Eq. (10.47) areobtained. If only a fraction k links coil 1 and coil 2, we get
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