Application of a conformal-mapping technique to a boundary-value problem of current distribution in plain conductors

Elimination of Current Crowding Problem in Flat Conductors Bent at Arbitrary Angles

“…Moreover, a dependence between the radius of an arc and the current density has been found. The obtained results may be used in connection with results of work [6] to calculate current density distributions in flat conductors with complex geometry. The conformal mapping technique utilized in our paper is applicable to two-dimensional problems but we hope that the presented results will also be helpful for numerical investigation of three-dimensional conductors.…”

“…These two functions are related with the Cauchy-Riemann equations, therefore, boundary conditions may be written only for one of them. The boundary conditions require the absence of the current flow through lateral boundaries of the conductor; so the resulting boundary value problem is as follows [6]: The solution of this problem can be found by mapping a complex potential of a two-dimensional charge placed at the origin of an upper complex half-plane…”

“…The conductors are supposed to be infinite on both sides with a current strength applied at the infinity. On the one hand, such form of conductors allows the application of analytical methods, on the other, it may be used as a part of more complex constructions adopting the technique described in our previous work [6].…”

Application of conformal mapping technique to problems of direct current distribution in thin film wires bent at arbitrary angle

“…These two functions are bound with Cauchy-Riemann conditions therefore a boundary conditions can be written only for one of them. The boundary conditions requires the absence of a current flow through lateral boundaries of the conductor so the resulting boundary value problem is the following [3] Figure 1. The geometry of considered conductor.…”