Example-1: Magnetic circuit of an inductor
An electromagnetic device is shown in Figure 4.5. This is an inductor formed
by a winding and a magnetic core made of steel. There is an airgap in the core.
The core is of uniform cross section and the number of turns in the winding
is N. Input current I into the winding, and the magnetic fi eldisthusexcited
in the core as shown in Figure 4.5. To simplify the analysis, it is assumed
that the permeability of the steel is in fi nite, and the magnetic fi eld distributed
evenly in the core and airgap, and there is no leakage fi eld in the airgap.
Figure 4.5: Magnetic circuit of an inductor
Using Ampere's law, the relationship between the magnetic fl ux and current
can be described by the following close loop line integration
H.dl = NI,
where N is the number of turns in the winding, and I is the current going
through the winding.
Use the middle line of the core as the integration line l. Since the direction
of the fl ux intensity H isthesameasthatofdl, the integration can be simpli fi ed
H c L c + H g g = NI,
: fl ux intensity in the core,
: fl ux intensity in the airgap,
length of the core, and
length of the airgap.