In this paper we derived the formula for calculating the mutual inductance between circular filaments with lateral and angular misalignment by using the approach of the magnetic vector potential. The results obtained correspond to those of F. W. Grover, although the latter used the general formula given by the Neumann integral instead of a vector potential approach. However, the major purpose of this paper is to clarify some confusion introduced in previous works regarding the mutual inductance calculation between thin filamentary circular coils with parallel axes in air. This problem has been solved by Kim et al. (1997) using the magnetic vector potential, but unfortunately it leads to erroneous results, even for slight misalignments of the coils' center axes. This is why we chose to use the approach of the magnetic vector potential to show that, when properly derived, the results must indeed reduce to the well known F.W. Grover's formulas.
2. Butterworth, S., "On the coe±cients of mutual induction of eccentric coils," Philosophical Magazine, Vol. 31, 443-454, 1916.
3. Snow, C., Formulas for Computing Capacitance and Inductance, National Bureau of Standards Circular 544, Washington DC, 1954.
4. Grover, F. W., "The calculation of the mutual inductance of circular lilaments in any desired positions," Proceedings of the I.R.E., 620-629, 1944.
5. Grover, F. W., Inductance Calculations, Dover, New York, 1964.
6. Kalantarov, P. L., Inductance Calculations, National Power Press, Moscow, 1955.
7. Dwight, H. B., Electrical Coils and Conductors, McGraw-Hill Book Company, New York, 1945.
8. Kim, K. B., E. Levi, Z. Zabar, and L. Birenbaum, "Mutual inductance of noncoaxial circular coils with constant current density," IEEE Trans. Mag., Vol. 33, No. 5, 3916-3921, 1997.
9. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Vol. 55, 595, National Bureau of Standards Applied Mathematics, Washington DC, 1972.
10. Gradshteyn, I. S. and I. M. Rhyzik, Tables of Integrals, Series and Products, Dover, New York, 1972.
11. Akyel, C., S. I. Babic, and M. M. Mahmoudi, "Mutual inductance calculation for non-coaxial circular air coils with parallel axes," Progress In Electromagnetics Research, Vol. 91, 287-301, 2009.
12. Conway, J. T., "Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils," IEEE Trans. Mag., Vol. 44, No. 4, 453-462, 2008.