A new electromagnetic model is established based on an average rate of directional time-distance energy transfers. A directional time-distance energy transfer is defined as an energy carrier mediator (boson) exchange. Electromagnetic force is modeled as mean valued, continual emission and absorption of energy carrier mediators.

For an isolated, spherically symmetric static charge distribution, Maxwell's stress equation is recast using a variant of Stokes' Theorem. The recast stress equation eliminates the stress normal to the electric field and establishes 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 is recast using a variant of Stokes' Theorem. The recast stress equation develops 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.

For an isolated, differential current element, Maxwell's stress equation is recast using a variant of Stokes' Theorem. The recast stress equation establishes a pinch stress that is normal to the magnetic field and is directed inward toward the differential current element. Similar to the Poincaré stress, the pinch stress is omnidirectional and is modeled as a mean valued, continual exchange of bosons between the current element and the distant matter of the universe.

For two separated, static differential current elements, a Neumann stress is established by analyzing the historical current force formulas known to be compatible with Maxwell's equations for closed circuits. The term Neumann stress is assigned to the line stress that only exists at each point on the straight path between two separated, differential current elements. Similar to the Coulomb stress, the Neumann stress is modeled as a mean valued, continual exchange of photons back and forth between two differential current elements in opposite directions.