Ampere’s law

Ampere’s law is the most important law concerning magnetic circuits in a motor or transformer, which is given by:

H=Magnetic field intensity vector (A/m)
dl=Line-element vector along the integration loop (m)
N=Number of winding turns
I= Electric current (A)
・：Vector inner product

For example, the integral of the vector dot product along the blue closed loop in the figure (on the left side) is equal to

NI. This is the sum of the currents in the integration path and is called the magnetomotive force. Here, it is the product of the current I and the number of winding turns N.
In the figure below, a simple law for determining the magnetic field strength Hg of the gap (section δ) can be obtained by choosing the integral path through the armature core, the air gap and the yoke.

By ignoring Hi, the field intensity in the highly permeable core, we obtainHg=NI/2δ.