A General Mutual Inductance Formula for Parallel Non-coaxial Circular Coils

摘要

In this paper, we present a complete derivation of a new formula for calculating the mutual inductance between two parallel non-coaxial circular coils by using the magnetic vector potential. Although this problem has been studied by Kim et al, their formula is wrong when the two parallel circulars are non-coaxial. The newly derived formula can not only clarifies the origin of the error introduced in Kim's work, but also can be reduced to the well-known F. W. Grover formula. Different from the Grove's formula that has various cases of the singularities, the new formula enables to simplify all the singular cases into single situation. The singularity in our formula has the clearly geometrical significance, i.e., the point located in one projected circular coil overlapped with the center of another one, which can be easily tackled by the principal value integrals. In order to check the validity of our formula, we have investigated the mutual inductance of the circular coil of the rectangular cross section, and the results demonstrate the correctness of our formula as compared with the other approaches, such as the Neumann's formula, Grover's formula and other published data. In addition, our formula is capable of handling the topics involving the circular coils such as the coils of the rectangular cross section, wall solenoids, disk coils and circular filamentary coils etc. In conclusion, our newly derived formula is of great importance for the electromagnetic applications concerning the calculation of the mutual inductance of the two parallel non-coaxial circular coils.