Simple calculation of eddy currents in a long passive conductor

Current density in a group of long parallel conductors

“…This approach does not indicate a change in the original objective, i.e. determination of current density in conductors, as proved in [5].…”

“…edges is a path graph [5,13]. Similarly, as a generalization of the results in [5], the conductors are numbered in each pair of aggregates A ( ) a ℓ , a A ( ) + ℓ 1 , ℓ=1, 3, K, c2−1, connected to the same source. The graph with…”

“…The method proposed is a generalization of the method for calculating current density in a conductor that is not connected to a source and lies in an external time-varying magnetic field. This method was published in [5]. The currents, voltages and magnetic fields are assumed to be quasistationary and the displacement current is neglected.…”

“…Generally, the conductors considered are A ℓ , where ℓ=1, 2, K, c, c>0. Each cross section A ℓ is in fact a closed connected set with continuous boundary [6] and thus it can be approximated with arbitrary precision by the cross section A ( ) a ℓ , which is a sum of disjoint rectangles [5]. These rectangles can form part of the net R of identical rectangles formed with the aid of the parallels…”

Transient Current Density in a Pair of Long Parallel Conductors

“…The differentiation of a function with respect to time t is denoted by a dot over the symbol of the function. The coefficients φ ik do not depend on t, and their calculation is described in the Appendix of [9]. J k (t)(z 2 − z 1 )µ 0 φ ik /(4π) is the contribution of the kth partial conductor to the magnetic flux through the segment (between the planes z = z 1 and z = z 2 ) of the loop formed by partial conductors A i and A i+1 .…”