Similarly, in 6, solving the problem in terms of the magnetic scalar potential
, the authors propose a method for replacing a laminated medium so that an adequate reflection of the magnetic field is achieved in the problems of magnetostatics.
Since [bar.B] = [nabla] x [bar.A] where [bar.A] is the magnetic vector potential, then the mathematical model of the eddy current results can be described by means of the complex magnetic vector potential [bar.A] and a complex scalar potential [phi] (where 9 is the magnetic scalar potential
H = -[nabla][phi]):
In the above equation, H = f(B) denotes the interpolation function of test B-H curve and [phi] denotes the magnetic scalar potential
. In a 2D axisymmetric case, (8) could be derived as the following wave equation:
The magnetic scalar potential
is due to a continuous distribution of matter; for example, earth may be calculated at an external point P (Figure 2) 26, 27].
Note that in a transverse plane, where H is a gradient field, the concept of magnetic voltage is equivalent to magnetic scalar potential
According to the scale magnetic potential method , for permanent magnet sheet, the magnetic scalar potential
[phi] within the sheet obey Poisson's equation:
This means using magnetic vector potential in [[OMEGA].sub.c] together with scalar electric potential combined with the use of magnetic scalar potential
in the non-conducting area (Ciric, 2007).
2) Magnetic scalar potential
[U.sub.m] of the ferromagnetic pole shoes on the N-pole magnet surface [U.sub.m1] = + [F.sub.m], that on the S-pole magnet surface [U.sub.m2] =- [F.sub.m], and on the stator surface [U.sub.m3] = 0 (Fig.
Finally, a magnetic scalar potential
[psi] is defined in
where [phi] is the magnetic scalar potential
and [rho] = [square root of ([y.sup.2] + [z.sup.2])] is the axial radius coordinate.
Together with the divergence theorem and the jump condition on the normal magnetic field across the surface, the magnetic scalar potential
[[phi].sup.e] satisfies a boundary integral equation written as: