Magnetostatic Stress: Insightful Analysis and Manipulation of Maxwell's Stress Equation for Magnetostatics

A pictorial view of the relationship between magnetic flux and the inductance terms of two coaxial current loops in free space

“…In this case, the magnetostatic potential energy may be viewed as being stored in the current distribution itself. A third way of viewing the magnetostatic potential energy is a mean valued continual exchange of energy carrier mediators (i.e., trapped energy) between certain current carrying conductor elements pairs, resulting in a repulsive force between them or a missing exchange of energy carrier mediators (i.e., missing energy) between other current carrying conductor elements pairs resulting in these being pushed together [41,42]. The continual exchange and missing exchange of energy carrier mediators accounts for the net positive valued self and mutual magnetostatic potential energy of the two current loops as well as the two current loops being pushed together.…”

“…. As such, the differential element of magnetostatic potential energy corresponding to the general differential current element force formula of (36) could just as well be: and the magnetostatic potential energy corresponding to the Moon and Spencer differential current element force formulas of (37) could just as well be: Using a similar process found in prior work of computing the magnetostatic potential energy between various closed loops [43], the constraints on k 1 , k 2 , and k 3 of ( 36), ( 37), (42), and ( 43 , the end result is an attractive force between the two current loops of figure 1 and the correct positive valued mutual magnetostatic potential energy associated with the two loops.…”

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.…”