an investigation of dual stator winding induction machines

Definition 3.2:
If E is the electric field in the area, O is the boundary of the area S, then from
Stoke's theorem, the following property can be established:
∫
O
E ⋅ dl = 0
(3.3)
Definition 3.3: Ampere's Law
Ampere's law is the fundamental basis on which we begin our electric machine design
and analysis. It can be expressed as:
∇ 0
× B = µ ⋅ J
(3.4)
where, B is the magnetic flux density, J is the current density and µ 0 is the
permeability of free space.
Doing integration on both sides of equation (3.4) over an arbitrary finite open surface:
∫
S
∇ ×
∫
B 0
S
⋅ ds = µ J ⋅ ds
(3.5)
By Stoke's theorem, the left side of equation (3.5) can be altered to the form:
∫
S
∫
∇ × B ⋅ ds = B ⋅ dl
(3.6)
O
The right side of equation (3.5) is obviously proportional to the current flowing
through the surface S . Then a simple format of the integration of Ampere's law can be
expressed as:
∫ B ⋅ dl = µ 0I
(3.7)
O
If the behavior of the magnetic field in the material bodies is considered, the usual
format of the integration of Ampere's law can be expressed as:
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