A boson interaction model for electrostatic stresses

Abstract

Maxwell's stress equation for electrostatics identifies a tensile stress in the direction of the electric field and a pressure normal to this direction. For an isolated, spherically symmetric static charge distribution, Maxwell's stress equation may be recast to eliminate the stress normal to the electric field and establish a stress only aligned with the electric field. The remaining stress is identified as an external omnidirectional Poincaré stress, inwardly directed towards the charge distribution. The Poincaré stress is modeled as a mean valued, continual exchange of bosons between the charge distribution and the distant matter of the universe. For two separated, spherically symmetric static charge distributions, Maxwell's stress equation may be recast to develop a line stress that only exists on the straight path between the two charge distributions. The line stress is identified as a Coulomb stress modeled as a mean valued, continual exchange of photons back and forth between two like-charge distributions.

A magnetic vector potential corresponding to a centrally conservative current element force

“…As described in section 4 further, for magnetostatics the centrally conservative force is adduced when the magnetostatic potential energy is modeled as a mean valued continual exchange of energy carrier mediators (i.e., trapped or positive valued energy) between repelled current carrying conductor element pairs, resulting in these being pushed apart; or a missing exchange of energy carrier mediators (i.e., missing or negative valued energy) between attracted current carrying conductor element pairs resulting in these being pushed together [27][28][29]. This model is describe in greater detail in section 4.…”

“…The boson interaction model for electrostatics is highlighted first. Maxwellʼs stress equation for two differential charge elements may be mathematically manipulated into two types of stresses: (1) an omnidirectional inward stress/pressure proportional to the total (self and interaction) electrostatic potential energy of the two differential charge elements and (2) a line stress between the two charge elements proportional to the Coulomb force [39,40]. The details of the mathematical manipulation and resulting mathematical stresses are not repeated here.…”

“…There are two aspects to the mean valued continual exchange of photons to and from charge elements for the boson interaction electrostatic model. The first is associated with an external exchange to and from a given charge distribution and is coined the term Poincaré stress [39,40]. The second is associated with an internal exchange between individual charge elements and is coined the term Coulomb stress [39,40].…”

“…The first is associated with an external exchange to and from a given charge distribution and is coined the term Poincaré stress [39,40]. The second is associated with an internal exchange between individual charge elements and is coined the term Coulomb stress [39,40].…”

“…The Poincaré stress represents an inwardly directed, external omnidirectional stress proportional to the electrostatic potential energy of the charge distribution and is mathematically compatible with Maxwellʼs stress equation [39,40]. In general, the Poincaré stress is a binding force that keeps a charge distribution stable [44,45] and is typically viewed as being internal to the charge distribution (i.e., an inward pulling force equalizing the outward electrostatic pressure).…”