Generalised solution of field distribution in cylindrical shells of finite length and thickness due to axial currents

A cylindrical conducting shell of finite length and finite thickness, surrounding a straight current filament of infinite length, is considered. This current filament is assumed to be parallel to the axis of the cylinder, and generally at an arbitrary distance from it. Because of the presence of this excitation, eddy currents are induced within the conducting material of the shell. Using the wave equation instead of thee diffusion differential equation a generalised solution of the field equations is formed by taking into account the term corresponding to the displacement current. This rigorous approach leads to an accurate determination of the eddy currents´ distribution within the conducting material of the shell, as well as the magnetic-flux-density distribution in the air regions both inside and outside the cylindrical shell.