Accurate off-axis magnetic field calculation of axisymmetric cylindrical current distributions

This paper proposes an accurate, simple, and versatile approach for calculation of the off-axis magnetic field of any axisymmetric cylindrical current distribution, eliminating the need for complicated elliptical integrals and sophisticated numerical methods, e.g., finite element method. The results obtained from both integral and series forms not only confirm the validity of the proposed method against well-established analytical techniques but also outperform them in terms of accuracy, simplicity, and calculation time. The integral method yields greater convergence (14 decimal places) compared to the ill-posed series method, which depends on the highest order of derivatives; this would yield an error below 1% at the highest order of derivatives (i.e., 14 for axial-H and 11 for radial-H in the range of 0 < ρ < 0.8R). The off-axis solution to the case of a thin shell of finite length with cylindrical current distribution is calculated using the proposed method irrespective of the current density function, though only the most common case of uniform current has been included in the solved special cases. Given that no known formula is available to solve this case, the results of this work have been validated against the results of the well-known software ANSYS Maxwell simulator.