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 difference.

According to the scale magnetic potential method [17], 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: