Field and inductance of circular coils placed eccentrically inside a cylindrical screen of finite length and high permeability

Abstract

For the circular coils of parallel axes eccentrically placed inside a cylinder of finite length and high permeability, the magnetic field and inductance are discussed and the analytic solutions are given by introducing a proper ansatz of the magnetic scalar potential (MSP), which is easy to satisfy the boundary conditions on the surface of the cylinder. By the separation of the total axial field into the source and secondary parts, the axial factor of the ansatz can be obtained, and the coefficients of the ansatz can be further found out by using the spring characteristics of the MSP. The results are further developed to find the self- and mutual inductance of the shielded circular rings and coils with rectangular cross section by calculating the corresponding magnetic flux. In addition, for the general case of the coils with parallel axes, the numerical results of the proposed method are compared with those of the finite element method simulations. For the special case of the rings coaxial with the cylinder, the results of our method are compared with those of the literature. Finally, the validity of our method is confirmed by the good agreement between them in the numerical calculations in all cases.