An Image Method for Evaluating Partial Inductance in Conducting Half-Space

Partial inductances are required in the circuit-based models of wire-like structures within a conducting half-space. Different approaches were used to calculate partial inductances, which mainly varied between applying or not applying the mirror image theory. The mirror image theory is applied to the electric field; however, the rigorous analysis in this article shows that it does not hold for the magnetic field in the general case. This article introduces an accurate image method developed for the magnetic field in a conducting half-space suitable for practical computations. New closed-form formulas for partial inductances were derived for some typical cases, but for the general case with conductors in arbitrary positions, it is more efficient to use numerical integration. For such a purpose, a MATLAB script is provided. It has been shown that frequently used approximations can lead to significant errors.