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Abstract
The magnetic field of the circular coils shielded by a coaxial cuboid of high permeability is investigated and the field solutions are given by introducing a proper ansatz of the magnetic scalar potential (MSP), which is convenient to fulfill the boundary conditions on the surfaces of the cuboid. The axial factor of the ansatz is obtained by separating the total axial field into the primary and secondary parts, and the coefficients of the ansatz are found out with the help of the spring properties of the MSP and the orthogonal relation of the eigenfunctions. The results are further developed to obtain the self- and mutual inductance of the shielded coaxial circular coils with rectangular cross section by calculating the associated magnetic flux. Finally, the numerical results of the proposed method are compared with those of the finite element method (FEM) simulations, and the validity of our method is confirmed by the high consistency between them in all cases.