Some remarks about flux linkage and inductance

In the area of computational electromagnetics there is an increasing demand for various coupled simulations. One example is the coupling between field and circuit simulation for the description of electromagnetic devices. In the context of such couplings, theoretical questions arise as well. How can a field device be represented as an equivalent multiport circuit element? What is meant by flux linkage if the considered conductors are not filamentary? What is meant by inductance if the magnetic media exhibit nonlinear behaviour? These questions and their answers are not new. However, according to the author’s view, these issues are not sufficiently addressed in the usual textbooks. The aim of the paper is therefore to (hopefully) answer the questions concisely and correctly. The modern language of differential forms will be employed for this purpose.