Three-dimensional analog of the Cauchy integral formula for solving magnetic field problems

摘要

Lately, the three-dimensional (3-D) analog of the Cauchy integral formula was used for several studies in geophysics and magnetism. In this paper, a simple demonstration of the expression of the 3-D analog of the Cauchy integral formula is given using only the usual rules of vector calculus, whereas the demonstrations given in references such as journal papers, treatises, or textbooks require complicated mathematical proceedings and lack clearness. Further on in the paper it is shown that some formulas obtained in references by using the analog of the Cauchy integral formula include inadequate results. The ways to avoid these inadequate results are also shown.