Eddy Currents and Magnetic Field Calculation in a Conductive Rod of Finite and Infinite Length Wrapped by a Cylindrical Coil

In this paper, we present a two-dimensional analytical model for an axisymmetric problem that enables the calculation of the magnetic field and eddy currents in a conducting rod surrounded by a cylindrical coil, for both finite and infinite length cases. The analytical model for the finite length case is based on a solution that combines the approach of separation of variables and the Truncated Region Eigenfunction Expansion method (TREEM). This approach allows solving the Laplace, Helmholtz, and Poisson equations formulated within the framework of the magnetic vector potential (MVP). This analytical model takes into account the effects of longitudinal ends in the case of a conductive rod of finite length, but does not include them for the case of infinite length. Furthermore, it computes the complex eigenvalues generated by a nonlinear trigonometric equation. The results of the analytical model's computation are compared with those obtained using the finite element method (FEM).