Electrostatics

Gravistatics

Like charges repel

Like planckion masses repel and attract,

Unlike charges attract

Unlike planckion masses attract and repel, indirectly

Fluid forces acting on each species, the positive, and the negative mass planckions

$\overrightarrow{E}=\overrightarrow{E^{\left(0\right)}}-\overrightarrow{E^{\left(1\right)}}$

$\overrightarrow{g}=\overrightarrow{g^{\left(0\right)}}+\overrightarrow{g^{\left(1\right)}}$

$=\left(K-\chi \right)\overrightarrow{E}$

$=\left(K+\chi \right)\overrightarrow{g}$

$\overrightarrow{E}=\overrightarrow{E^{\left(0\right)}}/K<\overrightarrow{E^{\left(0\right)}}$ (screening)

$\overrightarrow{g}=\overrightarrow{g^{\left(0\right)}}/K>\overrightarrow{g^{\left(0\right)}}$ (anti-screening)

$\overrightarrow{P}={\epsilon }_0\chi \overrightarrow{E}={\epsilon }_0\overrightarrow{E^{\left(1\right)}}$

$\overrightarrow{P}={\epsilon }_0\chi \overrightarrow{g}={\epsilon }_0\overrightarrow{g^{\left(1\right)}}$

$k=1/\left(4\pi {\epsilon }_0\right)=8.99\text{E}9\left(\text{MKS}\right)$

$G_0=1/\left(4\pi {\epsilon }_0\right)=6.67\text{E}-11\left(\text{MKS}\right)$

$\overrightarrow{\nabla }\cdot \overrightarrow{P}={\rho }_B$

$-\overrightarrow{\nabla }\cdot \overrightarrow{P}={\rho }_B$

${\displaystyle \oint \overrightarrow{P}\cdot \overrightarrow{\text{d}A}}=Q_B$

$-{\displaystyle \oint \overrightarrow{P}\cdot \overrightarrow{\text{d}A}}=M_B$

$\overrightarrow{D}={\epsilon }_{0}K\overrightarrow{E}={\epsilon }_0\overrightarrow{E^{\left(0\right)}}$

$\overrightarrow{D}={\epsilon }_{0}K\overrightarrow{g}={\epsilon }_0\overrightarrow{g^{\left(0\right)}}$

$\overrightarrow{\nabla }\cdot \overrightarrow{D}={\rho }_F$

$-\overrightarrow{\nabla }\cdot \overrightarrow{D}={\rho }_F$

${\displaystyle \oint \overrightarrow{D}\cdot \overrightarrow{\text{d}A}}=Q_F$

$-{\displaystyle \oint \overrightarrow{D}\cdot \overrightarrow{\text{d}A}}=M_F$

$\overrightarrow{\nabla }\cdot \left({\epsilon }_0\overrightarrow{E}\right)={\rho }_F-{\rho }_B$

$-\overrightarrow{\nabla }\cdot \left({\epsilon }_0\overrightarrow{g}\right)={\rho }_F+{\rho }_B$

${\displaystyle \oint \left({\epsilon }_0\overrightarrow{E}\right)\cdot \overrightarrow{\text{d}A}}=Q_F-Q_B$

$-{\displaystyle \oint \left({\epsilon }_0\overrightarrow{g}\right)\cdot \overrightarrow{\text{d}A}}=M_F+M_B$

$\overrightarrow{E}=\overrightarrow{E^{\left(0\right)}}-\overrightarrow{E^{\left(1\right)}}$

$\overrightarrow{g}=\overrightarrow{g^{\left(0\right)}}+\overrightarrow{g^{\left(1\right)}}$

can be written as,

can be written as,

$\left({\epsilon }_0\overrightarrow{E}\right)=\overrightarrow{D}-\overrightarrow{P}$

$\left({\epsilon }_0\overrightarrow{g}\right)=\overrightarrow{D}+\overrightarrow{P}$

$\overrightarrow{D}$ = electric displacement field

$\overrightarrow{D}$ = gravitational displacement field

$Q=Q_{TOTAL}=Q_F-Q_B$

$M=M_{TOTAL}=M_F+M_B$

$\rho ={\rho }_{TOTAL}={\rho }_F-{\rho }_B$

$\rho ={\rho }_{TOTAL}={\rho }_F+{\rho }_B$