where [nabla] is a differential operator of Hamilton; [bar.A] is a vector magnetic potential
; U is a scalar electric potential; [sigma] is the specific electrical conductivity of the medium.
For the section [S.sub.1], located in the plane of the negative values of X, the magnetic potential
vector would have two components, [??] and [??]:
Some examples of the distribution of magnetic field lines (tangent to the vector magnetic potential
A) and magnetic field induction B are shown in Fig.
395 that "The magnetic potential
, as thus defined [by its integral expression], is found by the same mathematical process, whether the given point is outside the magnet or within it." He then has the problem of relating this "mathematically defined" continuum field to something that can be measured experimentally (at least, in principle).
When coil turns remain unchanged, the increase of drive current increases the magnetic potential
. This increases the magnetic induction intensity at the working air gap, thereby increasing electromagnetic force.
In a current free region, where [nabla] x H = 0 and H is magnetic field strength, it is possible to define a scalar magnetic potential
[V.sub.m] from the relation H = [nabla][V.sub.m].
Considering Coulomb criteria, [nabla]A=0, Maxwell's equations to calculate the magnetic potential
of the PMs can be expressed by Laplace and Poisson partial differential equations as below :
According to the scale magnetic potential
method , for permanent magnet sheet, the magnetic scalar potential [phi] within the sheet obey Poisson's equation:
We can use image theory and superposition as in the case of the tangential dipole to compute the magnetic potential
of the resulting composite loop in z > 0 or z < 0.
Generally, there are no electric power and magnetic source inside the sensor, and the electrical potential [phi] and magnetic potential
F within the flow area satisfy the Laplace' equations,
The magnetic induction and the magnetic field intensity are calculated using the vector magnetic potential
Life's magnetic potential
is so great that we can even defy gravity under the right circumstances.