Electrodynamic Interaction Forces between Current Carrying Conductors for Different Mutual Arrangements

The problem of determining the electrodynamic forces arising between rectilinear conductors with currents through them for different cases of their mutual arrangement is addressed. The works published on this matter require further elaboration of particular cases for the purpose of practical application, in view of the lack of a general statement of the problem, theoretical justification, and the possibility of considering the entire variety of implementations. The article presents general and particular results for determining, in vector form, the electrodynamic forces acting on rectilinear conductors with currents through them. Simple expressions for degenerate and boundary cases of infinite and finite length conductors are considered, which give insight into the dominant forces and emphasize important aspects of the interactions. The difference in approaches to determining the electrodynamic forces between parallel conductors by direct calculation and when predicting them by using the energy method (through finding the mutual induction coefficient derivative with respect to the generalized coordinate) is shown. The mutual arrangement cases considered are supported by with explanatory figures and detailed conclusions. The presented expressions are recommended for practical use and can be applied for calculating shock and vibration effects on the busbar and individual cores of three-phase cables at the places in which they are connected to the switchgear in autonomous power supply systems, although they do not exclude the need to state the problem in general form.