A note on the analysis of the fields of line currents and charges

The method of images is widely used in the analysis of fields due to currents and charges, but it is of limited application and a more general method is required. It is the object of the paper to show that, for the analysis of 2-dimensional fields due to linear filaments of current or charge, conformal-transformation methods can be used simply for a very wide range of problems; the only requirement is the determination of an equation (or a series of equations) which transforms a straight line into the shape of the boundary of the field. The boundary types which can be treated simply are equipotential, flux-line, and combinations of the two. The necessary basic field solutions for each of these three types, for fields interior and exterior to given boundaries, are developed. Use of the method is demonstrated with two examples involving simple polygonal boundaries. The first is a determination of the error caused by treating a finite boundary as if it were infinite (an approximation frequently necessary when the image method is used). The second is an estimation of the inductance of a conductor carrying high-frequency alternating current and influenced by a conducting surface. A method of estimating the inductance of a conductor influenced by permeable bodies is also mentioned.