In this expression, P(r) is the electric charge density
at the point r and [epsilon] is the permittivity of the surrounding medium.
He derives the potential of a point charge and a sum of point charges in free space for the electric field defined in (5); then generalizes this potential to an integral over a volume V of electric charge density
[[rho].sub.e] and defines the potential for the point of observation r everywhere including points within the charge density of V to get [1, Arts.
Discretized Electric Charge Density
. In this subsection, we attempt to discrete the electric charge density
The main trends of the electric charge density
for a given value of the fluid velocity are easily observed in Fig.
In vacuum where electric charge density
[rho] = 0 and electric current density J = 0, Eqs.
Quantity Form Type Units Vector/ Scalar Electric Field Intensity E one-form V E Magnetic Field Intensity H one-form A H Electric Flux Density D two-form C D Magnetic Flux Density B two-form Wb B Electric Current Density J two-form A J Electric Charge Density
Q three-form C P Table 2.
(8), we can obtain the unknown electric charge density
As stated in the introduction, the present theory is based on the hypothesis of a nonzero electric charge density
in the vacuum.
The nonzero electric field divergence further gives rise to a local intrinsic electric charge density
within the photon body, whereas there is a vanishing total charge of the latter.
The latter theory is based on a vacuum state that is not merely an empty space but includes the electromagnetic fluctuations of the zero point energy and a corresponding nonzero electric charge density
associated with a nonzero electric field divergence.
The zero-point-energy of the vacuum state, its related electromagnetic vacuum fluctuations, the Casimir effect, and the electron-positron pair formation out of the vacuum support the hypothesis of a local electric charge density
and an associated nonzero electric field divergence in such a state.
The basic physical concept of the present theory is the appearance of a local electric charge density
in the vacuum state in which there are quantum mechanical electromagnetic fluctuations.