Current distribution in a parallel set of conducting strips

Abstract

The current distribution in a parallel set of thin conducting sheets due to an external applied source is investigated. All sheets are placed in one plane. The source, and all excited fields, are time-harmonic. The frequency is low enough to allow for an electro quasi-static approximation (neglecting the displacement current). The conducting sheets are infinitely long and the current is uniform in the longitudinal direction of the sheets. The sheets have a thin rectangular cross-section, so thin that the current can be assumed uniform in the thickness-direction. Hence, the current distribution only depends on the transverse coordinate. Due to the mutual induction between the sheets, the current distribution over the width of the cross-section becomes non-uniform: it accumulates at the edges of the sheets. It is especially this so-called edge-effect, and its dependence on the applied frequency and the distances between the sheets, that is the aim of this investigation. From the Maxwell equations, a set of integral equations for the current distribution in the sheets is derived. These integral equations are solved, as far as possible by analytical means, by writing the current distribution in each sheet as a series of Legendre polynomials. The general method is worked out for N (N ≥ 1) sheets, but explicit results are presented for N=1 and 3. It turns out that the edge-effect becomes stronger for increasing frequencies. For this solution, only a very restricted number of Legendre polynomials are needed.