Now consider the case where the Hall's term (J x B/ne) may be neglected and where the gradient of pressure term may be replaced by the product of a scalar potential
and the gradient of a different scalar potential
, a Euler potential term (we will return to this correspondence later in the article).
Quaternionic version of Dirac equation in the presence of vector and scalar potential
can be written with the help of  as
The Klein-Gordon equation is formed by two potentials coupling which are the four-vector potential (V(r)) and scalar potential
The magnetic map may be considered the sum of a scalar potential
set assumed to be harmonic everywhere except above the ovens.
In some books and articles, the authors describe the magnetostatic field of magnetized bodies with the help of the scalar potential
[[phi].sub.m] which corresponds to the dipole model, and the magnetization [??] is used in the formulas for determining [[phi].sub.m].
This equation suffers from the low-frequency breakdown problem, because the contribution of the vector potential is swamped by that of the scalar potential
at low frequencies due to the finite machine precision.
where, [[rho].sub.0] is the density of proper mass in a distribution or system, [[nabla].sup.2] is the pure Euclidean Laplacian, G is the universal gravitational constant and f is the gravitational scalar potential
In conventional EEG the scalar potential
, obtained from current measurements, is recorded, and not the electric field.
Due to spherical symmetry of embryo and this fact that induced electrical field in mother body in z direction is constant, we have following equation (equation 1) for scalar potential
It can be shown that with the proper gauge, which is an extension of the simple Lorenz gauge  to inhomogeneous anisotropic media, the scalar potential
equation is decoupled from the vector potential equation .
Here, the Neumann relation is obtained by calculating the scalar potential
using Coulomb's law at the surface of the i-th wire caused by the charge in the j-th wire.