Analysis of Magnetic Field of Thin-Wall Air Induction Coil of Arbitrary Cross Section With the Help of Scalar Magnetic Potential

The analysis of magnetic field of a thin-wall air induction coil with a shape of finite cylinder of arbitrary cross section is described. The result of the analysis is a method for finding the scalar magnetic potential of the coil with the help of mutual inductance of the coil and the elementary loop. The magnetic flux density of the coil is found as the gradient of the scalar magnetic potential. The proposed analysis is verified using two examples, which are thin-wall air coils with a shape of finite cylinder of circular and rectangular cross sections. The magnetic flux density calculated by the presented method is compared with other approaches for both examples with excellent agreement.